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Journal articles on the topic 'Points semistables'

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Published: 30 November 2024
Last updated: 31 July 2025

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1

Luks, Tomasz, and Yimin Xiao. "Multiple Points of Operator Semistable Lévy Processes." Journal of Theoretical Probability 33, no. 1 (2018): 153–79. http://dx.doi.org/10.1007/s10959-018-0859-4.

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2

Heinzner, Peter, and Henrik Stötzel. "Semistable points with respect to real forms." Mathematische Annalen 338, no. 1 (2006): 1–9. http://dx.doi.org/10.1007/s00208-006-0063-1.

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3

Pattanayak, S. K. "Minimal Schubert Varieties Admitting Semistable Points for Exceptional Cases." Communications in Algebra 42, no. 9 (2014): 3811–22. http://dx.doi.org/10.1080/00927872.2013.795578.

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4

Castella, Francesc. "ON THE EXCEPTIONAL SPECIALIZATIONS OF BIG HEEGNER POINTS." Journal of the Institute of Mathematics of Jussieu 17, no. 1 (2016): 207–40. http://dx.doi.org/10.1017/s1474748015000444.

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We extend the $p$-adic Gross–Zagier formula of Bertolini et al. [Generalized Heegner cycles and $p$-adic Rankin $L$-series, Duke Math. J.162(6) (2013), 1033–1148] to the semistable non-crystalline setting, and combine it with our previous work [Castella, On the $p$-adic variation of Heegner points, Preprint, 2014, arXiv:1410.6591] to obtain a derivative formula for the specializations of Howard’s big Heegner points [Howard, Variation of Heegner points in Hida families, Invent. Math.167(1) (2007), 91–128] at exceptional primes in the Hida family.
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5

Lai, K. F. "C2 building and projective space." Journal of the Australian Mathematical Society 76, no. 3 (2004): 383–402. http://dx.doi.org/10.1017/s1446788700009939.

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AbstractWe study the stability map from the rigid analytic space of semistable points in P3 to convex sets in the building of Sp2 over a local field and construct a pure affinoid covering of the space of stable points.
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6

Abramovich, Dan, and Anthony Várilly-Alvarado. "Campana points, Vojta’s conjecture, and level structures on semistable abelian varieties." Journal de Théorie des Nombres de Bordeaux 30, no. 2 (2018): 525–32. http://dx.doi.org/10.5802/jtnb.1037.

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7

Tamagawa, Akio. "Ramification of torsion points on curves with ordinary semistable Jacobian varieties." Duke Mathematical Journal 106, no. 2 (2001): 281–319. http://dx.doi.org/10.1215/s0012-7094-01-10623-6.

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8

Vyugin, Il'ya Vladimirovich, and Lada Andreevna Dudnikova. "Stable vector bundles and the Riemann-Hilbert problem on a Riemann surface." Sbornik: Mathematics 215, no. 2 (2024): 141–56. http://dx.doi.org/10.4213/sm9781e.

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The paper is devoted to holomorphic vector bundles with logarithmic connections on a compact Riemann surface and the applications of the results obtained to the question of solvability of the Riemann-Hilbert problem on a Riemann surface. We give an example of a representation of the fundamental group of a Riemann surface with four punctured points which cannot be realized as the monodromy representation of a logarithmic connection with four singular points on a semistable bundle. For an arbitrary pair of a bundle and a logarithmic connection on it we prove an estimate for the slopes of the ass
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9

Kalabušić, S., M. R. S. Kulenović, and E. Pilav. "Multiple Attractors for a Competitive System of Rational Difference Equations in the Plane." Abstract and Applied Analysis 2011 (2011): 1–35. http://dx.doi.org/10.1155/2011/295308.

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We investigate global dynamics of the following systems of difference equationsxn+1=β1xn/(B1xn+yn),yn+1=(α2+γ2yn)/(A2+xn),n=0,1,2,…, where the parametersβ1,B1,β2,α2,γ2,A2are positive numbers, and initial conditionsx0andy0are arbitrary nonnegative numbers such thatx0+y0>0. We show that this system has up to three equilibrium points with various dynamics which depends on the part of parametric space. We show that the basins of attractions of different locally asymptotically stable equilibrium points or nonhyperbolic equilibrium points are separated by the global stable manifolds of either sad
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10

Nayek, Arpita, and S. K. Pattanayak. "Torus quotient of Richardson varieties in orthogonal and symplectic grassmannians." Journal of Algebra and Its Applications 19, no. 10 (2019): 2050186. http://dx.doi.org/10.1142/s0219498820501868.

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For any simple, simply connected algebraic group [Formula: see text] of type [Formula: see text] and [Formula: see text] and for any maximal parabolic subgroup [Formula: see text] of [Formula: see text], we provide a criterion for a Richardson variety in [Formula: see text] to admit semistable points for the action of a maximal torus [Formula: see text] with respect to an ample line bundle on [Formula: see text].
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11

Chen, Huachen. "O’Grady’s birational maps and strange duality via wall-hitting." International Journal of Mathematics 30, no. 09 (2019): 1950044. http://dx.doi.org/10.1142/s0129167x19500447.

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We prove that O’Grady’s birational maps [K. G O’Grady, The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface, J. Algebr. Geom. 6(4) (1997) 599–644] between moduli of sheaves on an elliptic K3 surface can be interpreted as intermediate wall-crossing (wall-hitting) transformations at so-called totally semistable walls, studied by Bayer and Macrì [A. Bayer and E. Macrì, MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations, Inventiones Mathematicae 198(3) (2014) 505–590]. As a key ingredient, we describe the first totally semistable
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12

Voskuil, Harm. "On the action of the unitary group on the projective plane over a local field." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 62, no. 3 (1997): 371–97. http://dx.doi.org/10.1017/s1446788700001075.

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AbstractLet G be a unitary group of rank one over a non-archimedean local field K (whose residue field has a characteristic ≠ 2). We consider the action of G on the projective plane. A G(K) equivariant map from the set of points in the projective plane that are semistable for every maximal K split torus in G to the set of convex subsets of the building of G(K) is constructed. This map gives rise to an equivariant map from the set of points that are stable for every maximal K split torus to the building. Using these maps one describes a G(K) invariant pure affinoid covering of the set of stable
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13

HITCHING, GEORGE H. "RANK FOUR SYMPLECTIC BUNDLES WITHOUT THETA DIVISORS OVER A CURVE OF GENUS TWO." International Journal of Mathematics 19, no. 04 (2008): 387–420. http://dx.doi.org/10.1142/s0129167x08004716.

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The moduli space [Formula: see text] of rank four semistable symplectic vector bundles over a curve X of genus two is an irreducible projective variety of dimension ten. Its Picard group is generated by the determinantal line bundle Ξ. The base locus of the linear system |Ξ| consists of precisely those bundles without theta divisors, that is, admitting nonzero maps from every line bundle of degree -1 over X. We show that this base locus consists of six distinct points, which are in canonical bijection with the Weierstrass points of the curve. We relate our construction of these bundles to anot
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14

Disegni, Daniel. "The -adic Gross–Zagier formula on Shimura curves." Compositio Mathematica 153, no. 10 (2017): 1987–2074. http://dx.doi.org/10.1112/s0010437x17007308.

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We prove a general formula for the $p$-adic heights of Heegner points on modular abelian varieties with potentially ordinary (good or semistable) reduction at the primes above $p$. The formula is in terms of the cyclotomic derivative of a Rankin–Selberg $p$-adic $L$-function, which we construct. It generalises previous work of Perrin-Riou, Howard, and the author to the context of the work of Yuan–Zhang–Zhang on the archimedean Gross–Zagier formula and of Waldspurger on toric periods. We further construct analytic functions interpolating Heegner points in the anticyclotomic variables, and obtai
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15

Trautwein, Samuel. "Convergence of the Yang–Mills–Higgs flow on Gauged Holomorphic maps and applications." International Journal of Mathematics 29, no. 04 (2018): 1850024. http://dx.doi.org/10.1142/s0129167x18500246.

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The symplectic vortex equations admit a variational description as global minimum of the Yang–Mills–Higgs functional. We study its negative gradient flow on holomorphic pairs [Formula: see text] where [Formula: see text] is a connection on a principal [Formula: see text]-bundle [Formula: see text] over a closed Riemann surface [Formula: see text] and [Formula: see text] is an equivariant map into a Kähler Hamiltonian [Formula: see text]-manifold. The connection [Formula: see text] induces a holomorphic structure on the Kähler fibration [Formula: see text] and we require that [Formula: see text
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16

RYAN, TIM. "THE EFFECTIVE CONE OF MODULI SPACES OF SHEAVES ON A SMOOTH QUADRIC SURFACE." Nagoya Mathematical Journal 232 (September 4, 2017): 151–215. http://dx.doi.org/10.1017/nmj.2017.24.

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Let $\unicode[STIX]{x1D709}$ be a stable Chern character on $\mathbb{P}^{1}\times \mathbb{P}^{1}$, and let $M(\unicode[STIX]{x1D709})$ be the moduli space of Gieseker semistable sheaves on $\mathbb{P}^{1}\times \mathbb{P}^{1}$ with Chern character $\unicode[STIX]{x1D709}$. In this paper, we provide an approach to computing the effective cone of $M(\unicode[STIX]{x1D709})$. We find Brill–Noether divisors spanning extremal rays of the effective cone using resolutions of the general elements of $M(\unicode[STIX]{x1D709})$ which are found using the machinery of exceptional bundles. We use this app
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17

Heinzner, Peter, Gerald W. Schwarz, and Henrik Stötzel. "Stratifications with respect to actions of real reductive groups." Compositio Mathematica 144, no. 1 (2008): 163–85. http://dx.doi.org/10.1112/s0010437x07003259.

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AbstractWe study the action of a real reductive group G on a real submanifold X of a Kähler manifold Z. We suppose that the action of G extends holomorphically to an action of the complexified group $G^{\mathbb {C}}$ and that with respect to a compatible maximal compact subgroup U of $G^{\mathbb {C}}$ the action on Z is Hamiltonian. There is a corresponding gradient map $\mu _{\mathfrak {p}}\colon X\to \mathfrak {p}^*$ where $\mathfrak {g}=\mathfrak {k}\oplus \mathfrak {p}$ is a Cartan decomposition of $\mathfrak {g}$. We obtain a Morse-like function $\eta _{\mathfrak {p}}:=\Vert \mu _{\mathfr
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18

Corbera, Montserrat, Jaume Llibre, and Marco Antonio Teixeira. "Symmetric periodic orbits near a heteroclinic loop in formed by two singular points, a semistable periodic orbit and their invariant manifolds." Physica D: Nonlinear Phenomena 238, no. 6 (2009): 699–705. http://dx.doi.org/10.1016/j.physd.2009.01.002.

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19

Herrero, Andres Fernandez. "On automorphisms of semistable G-bundles with decorations." Advances in Geometry, July 18, 2023. http://dx.doi.org/10.1515/advgeom-2023-0016.

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Abstract We prove a rigidity result for automorphisms of points of certain stacks admitting adequate moduli spaces. It encompasses as special cases variations of the moduli of G-bundles on a smooth projective curve for a reductive algebraic group G. For example, our result applies to the stack of semistable G-bundles, to stacks of semistable Hitchin pairs, and to stacks of semistable parabolic G-bundles. Similar arguments apply to Gieseker semistable G-bundles in higher dimensions. We present two applications of the main result. First, we show that in characteristic 0 every stack of semistable
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20

Haulmark, M., and M. Mihalik. "Relatively hyperbolic groups with semistable peripheral subgroups." International Journal of Algebra and Computation, March 8, 2022, 1–31. http://dx.doi.org/10.1142/s0218196722500321.

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Suppose [Formula: see text] is a finitely presented group that is hyperbolic relative to [Formula: see text] a finite collection of finitely generated proper subgroups of [Formula: see text]. Our main theorem states that if each [Formula: see text] has semistable fundamental group at [Formula: see text], then [Formula: see text] has semistable fundamental group at [Formula: see text]. The problem reduces to the case when [Formula: see text] and the members of [Formula: see text] are all one ended and finitely presented. In that case, if the boundary [Formula: see text] has no cut point, then [
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21

Asai, Sota, and Osamu Iyama. "Semistable torsion classes and canonical decompositions in Grothendieck groups." Proceedings of the London Mathematical Society 129, no. 5 (2024). http://dx.doi.org/10.1112/plms.12639.

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AbstractWe study two classes of torsion classes that generalize functorially finite torsion classes, that is, semistable torsion classes and morphism torsion classes. Semistable torsion classes are parametrized by the elements in the real Grothendieck group up to TF equivalence. We give a close connection between TF equivalence classes and the cones given by canonical decompositions of the spaces of projective presentations due to Derksen–Fei. More strongly, for ‐tame algebras and hereditary algebras, we prove that TF equivalence classes containing lattice points are exactly the cones given by
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22

Biswas, Indranil, Swarnava Mukhopadhyay та Richard Wentworth. "A Hitchin connection on nonabelian theta functions for parabolic 𝐺-bundles". Journal für die reine und angewandte Mathematik (Crelles Journal), 14 вересня 2023. http://dx.doi.org/10.1515/crelle-2023-0049.

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Abstract For a simple, simply connected complex affine algebraic group 𝐺, we prove the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli spaces of semistable parabolic 𝐺-bundles for families of smooth projective curves with marked points.
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23

BÉRCZI, GERGELY, and FRANCES KIRWAN. "GRADED UNIPOTENT GROUPS AND GROSSHANS THEORY." Forum of Mathematics, Sigma 5 (2017). http://dx.doi.org/10.1017/fms.2017.19.

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Let $U$ be a unipotent group which is graded in the sense that it has an extension $H$ by the multiplicative group of the complex numbers such that all the weights of the adjoint action on the Lie algebra of $U$ are strictly positive. We study embeddings of $H$ in a general linear group $G$ which possess Grosshans-like properties. More precisely, suppose $H$ acts on a projective variety $X$ and its action extends to an action of $G$ which is linear with respect to an ample line bundle on $X$. Then, provided that we are willing to twist the linearization of the action of $H$ by a suitable (rati
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24

Li, Muxi, and Mao Sheng. "Characterization of Beauville’s Numbers via Hodge Theory." International Mathematics Research Notices, August 9, 2021. http://dx.doi.org/10.1093/imrn/rnab211.

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Abstract We provide a new Hodge theoretical characterization of the set of complex numbers that arises from the complete list, due to A. Beauville, of semistable families of elliptic curves over ${\mathbb {P}}^1$ with four singular fibers. The characterization is approached via a detailed analysis of the periodicity of the uniformizing Higgs bundle attached to ${\mathbb {P}}^1$ minus four points over the field of complex numbers.
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25

Doi, Mamoru, and Naoto Yotsutani. "Differential geometric global smoothings of simple normal crossing complex surfaces with trivial canonical bundle." Complex Manifolds 10, no. 1 (2023). http://dx.doi.org/10.1515/coma-2022-0143.

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Abstract Let X X be a simple normal crossing (SNC) compact complex surface with trivial canonical bundle which includes triple intersections. We prove that if X X is d d -semistable, then there exists a family of smoothings in a differential geometric sense. This can be interpreted as a differential geometric analogue of the smoothability results due to Friedman, Kawamata-Namikawa, Felten-Filip-Ruddat, Chan-Leung-Ma, and others in algebraic geometry. The proof is based on an explicit construction of local smoothings around the singular locus of X X , and the first author’s existence result of
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26

Greb, Daniel, and Christian Miebach. "Hamiltonian actions of unipotent groups on compact K\"ahler manifolds." Épijournal de Géométrie Algébrique Volume 2 (November 9, 2018). http://dx.doi.org/10.46298/epiga.2018.volume2.4486.

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We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric quotients that carry compactifiable K\"ahler structures obtained by symplectic reduction. The relation of our complex-analytic theory to the work of Doran--Kirwan regarding the Geometric Invariant Theory of unipotent group actions on projective varieties is discussed in detail. Comment: v2: 30 pages, final version as accepted by EPIGA
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27

Halpern-Leistner, Daniel, Andres Fernandez Herrero, and Trevor Jones. "Moduli spaces of sheaves via affine Grassmannians." Journal für die reine und angewandte Mathematik (Crelles Journal), February 20, 2024. http://dx.doi.org/10.1515/crelle-2023-0099.

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Abstract We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of Geometric Invariant Theory. We apply this to two familiar moduli problems: the stack of Λ-modules and the stack of pairs. In both examples, we construct a Θ-stratification of the stack, defined in terms of a polynomial numerical invariant, and we construct good moduli spaces for the open substacks of semistable points. One of the essential ingredients is the construction of higher-dimensional analogue
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28

Hahn, Marvin Anas. "Mustafin Models of Projective Varieties and Vector Bundles." International Mathematics Research Notices, July 5, 2021. http://dx.doi.org/10.1093/imrn/rnab148.

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Abstract Mustafin varieties are well-studied degenerations of projective spaces induced by a choice of integral points in a Bruhat–Tits building. In recent work, Annette Werner and the author initiated the study of degenerations of plane curves obtained by Mustafin varieties by means of arithmetic geometry. Moreover, we applied these techniques to construct models of vector bundles on plane curves with strongly semistable reduction. In this work, we take a Groebner basis approach to the more general problem of studying degenerations of projective varieties. Our methods include determining the
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29

Sh. Roitenberg, Vladimir. "On bifurcations of a periodic orbit tangent to switching lines at two points." University proceedings. Volga region. Physical and mathematical sciences, no. 1 (2025). https://doi.org/10.21685/2072-3040-2025-1-4.

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Background. Dynamic systems defined by discontinuous piecewise smooth vector fields on a plane are natural mathematical models of relay systems in automatic control theory. Periodic trajectories describe self-oscillations. Although a significant number of works have been devoted to the study of the birth of periodic trajectories, the description oftypical bifurcations is far from complete. The purpose of this research is to study bifurcations of periodic trajectories similar to bifurcations of double and triple cycles of a smooth dynamic system. Materials and methods. The method of point mappi
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30

Haiden, F., L. Katzarkov, and C. Simpson. "Spectral Networks and Stability Conditions for Fukaya Categories with Coefficients." Communications in Mathematical Physics 405, no. 11 (2024). http://dx.doi.org/10.1007/s00220-024-05138-9.

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AbstractGiven a holomorphic family of Bridgeland stability conditions over a surface, we define a notion of spectral network which is an object in a Fukaya category of the surface with coefficients in a triangulated DG-category. These spectral networks are analogs of special Lagrangian submanifolds, combining a graph with additional algebraic data, and conjecturally correspond to semistable objects of a suitable stability condition on the Fukaya category with coefficients. They are closely related to the spectral networks of Gaiotto–Moore–Neitzke. One novelty of our approach is that we establi
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31

Araujo, Carolina, Thiago Fassarella, Inder Kaur, and Alex Massarenti. "On Automorphisms of Moduli Spaces of Parabolic Vector Bundles." International Mathematics Research Notices, July 8, 2019. http://dx.doi.org/10.1093/imrn/rnz132.

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AbstractFix $n\geq 5$ general points $p_1, \dots , p_n\in{\mathbb{P}}^1$ and a weight vector ${\mathcal{A}} = (a_{1}, \dots , a_{n})$ of real numbers $0 \leq a_{i} \leq 1$. Consider the moduli space $\mathcal{M}_{{\mathcal{A}}}$ parametrizing rank two parabolic vector bundles with trivial determinant on $\big ({\mathbb{P}}^1, p_1,\dots , p_n\big )$ that are semistable with respect to ${\mathcal{A}}$. Under some conditions on the weights, we determine and give a modular interpretation for the automorphism group of the moduli space $\mathcal{M}_{{\mathcal{A}}}$. It is isomorphic to $\left (\frac
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32

Kučikienė, Domantė, Ravichandran Rajkumar, Katharina Timpte, et al. "EEG microstates show different features in focal epilepsy and psychogenic nonepileptic seizures." Epilepsia, January 30, 2024. http://dx.doi.org/10.1111/epi.17897.

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AbstractObjectiveElectroencephalography (EEG) microstate analysis seeks to cluster the scalp's electric field into semistable topographical EEG activity maps at different time points. Our study aimed to investigate the features of EEG microstates in subjects with focal epilepsy and psychogenic nonepileptic seizures (PNES).MethodsWe included 62 adult subjects with focal epilepsy or PNES who received video‐EEG monitoring at the epilepsy monitoring unit. The subjects (mean age = 42.8 ± 21.2 years) were distributed equally between epilepsy and PNES groups. We extracted microstates from a 4.4 ± 1.0
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