Готові списки джерел за темами / Fano fourfolds of K3 type / Статті в журналах
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Статті в журналах з теми "Fano fourfolds of K3 type"

Автор: Grafiati
Опубліковано: 5 жовтня 2024
Оновлено: 19 липня 2025

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1

Fu, Lie, Robert Laterveer, and Charles Vial. "Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type." Annali di Matematica Pura ed Applicata (1923 -) 200, no. 5 (2021): 2085–126. http://dx.doi.org/10.1007/s10231-021-01070-0.

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Анотація:
AbstractGiven a smooth projective variety, a Chow–Künneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin, Shen and Vial conjectured that hyper-Kähler varieties admit a multiplicative Chow–Künneth decomposition. In this paper, based on the mysterious link between Fano varieties with cohomology of K3 type and hyper-Kähler varieties, we ask whether Fano varieties with cohomology of K3 type also admit a multiplicative Chow–Künneth decomposition, and provide evidence by establishing their existence for cubic fourfold
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2

Laterveer, Robert. "On the Chow ring of certain Fano fourfolds." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 19, no. 1 (2020): 39–52. http://dx.doi.org/10.2478/aupcsm-2020-0004.

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Анотація:
AbstractWe prove that certain Fano fourfolds of K3 type constructed by Fatighenti–Mongardi have a multiplicative Chow–Künneth decomposition. We present some consequences for the Chow ring of these fourfolds.
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3

Mongardi, Giovanni. "On symplectic automorphisms of hyper-Kähler fourfolds of K3[2] type." Michigan Mathematical Journal 62, no. 3 (2013): 537–50. http://dx.doi.org/10.1307/mmj/1378757887.

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4

Laza, Radu, and Kieran O’Grady. "Birational geometry of the moduli space of quartic surfaces." Compositio Mathematica 155, no. 9 (2019): 1655–710. http://dx.doi.org/10.1112/s0010437x19007516.

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Анотація:
By work of Looijenga and others, one understands the relationship between Geometric Invariant Theory (GIT) and Baily–Borel compactifications for the moduli spaces of degree-$2$ $K3$ surfaces, cubic fourfolds, and a few other related examples. The similar-looking cases of degree-$4$ $K3$ surfaces and double Eisenbud–Popescu–Walter (EPW) sextics turn out to be much more complicated for arithmetic reasons. In this paper, we refine work of Looijenga in order to handle these cases. Specifically, in analogy with the so-called Hassett–Keel program for the moduli space of curves, we study the variatio
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5

Tanimoto, Sho, and Anthony Várilly-Alvarado. "Kodaira dimension of moduli of special cubic fourfolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 752 (2019): 265–300. http://dx.doi.org/10.1515/crelle-2016-0053.

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Анотація:
Abstract A special cubic fourfold is a smooth hypersurface of degree 3 and dimension 4 that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether–Lefschetz divisors {{\mathcal{C}}_{d}} in the moduli space {{\mathcal{C}}} of smooth cubic fourfolds. These divisors are irreducible 19-dimensional varieties birational to certain orthogonal modular varieties. We use the “low-weight cusp form trick” of Gritsenko, Hulek, and Sankaran to obtain information about the Kodaira dimension of {{\mathcal{C}}_{d}} . For example, if {d=6
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6

Pym, Brent. "Elliptic singularities on log symplectic manifolds and Feigin–Odesskii Poisson brackets." Compositio Mathematica 153, no. 4 (2017): 717–44. http://dx.doi.org/10.1112/s0010437x16008174.

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Анотація:
A log symplectic manifold is a complex manifold equipped with a complex symplectic form that has simple poles on a hypersurface. The possible singularities of such a hypersurface are heavily constrained. We introduce the notion of an elliptic point of a log symplectic structure, which is a singular point at which a natural transversality condition involving the modular vector field is satisfied, and we prove a local normal form for such points that involves the simple elliptic surface singularities$\widetilde{E}_{6},\widetilde{E}_{7}$and$\widetilde{E}_{8}$. Our main application is to the class
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7

Konovalov, V. A. "THE USE OF MARKOV ALGORITHMS FOR THE STUDY OF l-VOIDS IN BIG DATA OF SOCIO-ECONOMIC SYSTEMS. PART 2." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 217 (July 2022): 30–41. http://dx.doi.org/10.14489/vkit.2022.07.pp.030-041.

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Анотація:
The second part of the article is presented. Big data l-voids are considered using the N-scheme of the Markov algorithm. The diagrams of occurrences of l-voids in a semi-Eulerian cycle containing an Euler path, a matroid and an incomplete Fano matroid, minors K3, 3 and K5, an extra large cycle of occurrences are analyzed. An example of reconstructing a fragment of an incomplete Fano matroid with l-voids is considered. Examples are given for independent implementation of the method of filling the artificial intelligence database (AnwM f typeK) DB based on the results of the analysis of l-voids
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8

Kretschmer, Andreas. "The Chow ring of hyperkähler varieties of $$K3^{[2]}$$-type via Lefschetz actions." Mathematische Zeitschrift, September 9, 2021. http://dx.doi.org/10.1007/s00209-021-02846-z.

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Анотація:
AbstractWe propose an explicit conjectural lift of the Neron–Severi Lie algebra of a hyperkähler variety X of $$K3^{[2]}$$ K 3 [ 2 ] -type to the Chow ring of correspondences $$\mathrm{CH}^*(X \times X)$$ CH ∗ ( X × X ) in terms of a canonical lift of the Beauville–Bogomolov class obtained by Markman. We give evidence for this conjecture in the case of the Hilbert scheme of two points of a K3 surface and in the case of the Fano variety of lines of a very general cubic fourfold. Moreover, we show that the Fourier decomposition of the Chow ring of X of Shen and Vial agrees with the eigenspace de
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9

Höring, Andreas, and Saverio Andrea Secci. "FANO FOURFOLDS WITH LARGE ANTICANONICAL BASE LOCUS." Journal of the Institute of Mathematics of Jussieu, January 20, 2025, 1–31. https://doi.org/10.1017/s1474748024000604.

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Анотація:
Abstract A famous theorem of Shokurov states that a general anticanonical divisor of a smooth Fano threefold is a smooth K3 surface. This is quite surprising since there are several examples where the base locus of the anticanonical system has codimension two. In this paper, we show that for four-dimensional Fano manifolds the behaviour is completely opposite: if the base locus is a normal surface, and hence has codimension two, all the anticanonical divisors are singular.
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10

Huybrechts, Daniel. "Chow groups of surfaces of lines in cubic fourfolds." Épijournal de Géométrie Algébrique Special volume in honour of... (July 30, 2023). http://dx.doi.org/10.46298/epiga.2023.10425.

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Анотація:
The surface of lines in a cubic fourfold intersecting a fixed line splits motivically into two parts, one of which resembles a K3 surface. We define the analogue of the Beauville-Voisin class and study the push-forward map to the Fano variety of all lines with respect to the natural splitting of the Bloch-Beilinson filtration introduced by Mingmin Shen and Charles Vial.
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11

Gounelas, Frank, and Alexis Kouvidakis. "On some invariants of cubic fourfolds." European Journal of Mathematics 9, no. 3 (2023). http://dx.doi.org/10.1007/s40879-023-00651-y.

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Анотація:
AbstractFor a general cubic fourfold $$X\subset \mathbb {P}^5$$ X ⊂ P 5 with Fano variety F, we compute the Hodge numbers of the locus $$S\subset F$$ S ⊂ F of lines of second type and the class of the locus $$V\subset F$$ V ⊂ F of triple lines, using the description of the latter in terms of flag varieties. We also give an upper bound of 6 for the degree of irrationality of the Fano scheme of lines of any smooth cubic hypersurface.
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12

Li Bassi, Lucas. "GIT stable cubic threefolds and certain fourfolds of $K3^{[2]}$-type." Revista Matemática Iberoamericana, April 14, 2025. https://doi.org/10.4171/rmi/1553.

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Анотація:
We study the behaviour on some nodal hyperplanes of the isomorphism, described by Boissière–Camere–Sarti, between the moduli space of smooth cubic threefolds and the moduli space of hyperkähler fourfolds of K3^{[2]} -type with a non-symplectic automorphism of order three, whose invariant lattice has rank one and is generated by a class of square 6; along those hyperplanes, the automorphism degenerates by jumping to another family. We generalize their result to singular nodal cubic threefolds having one singularity of type A_{i} , for i=2, 3, 4 , providing birational maps between the loci of cu
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13

O'Grady, Kieran G. "Rank 4 stable vector bundles on hyperk\"ahler fourfolds of Kummer type." Épijournal de Géométrie Algébrique Special volume in honour of... (December 5, 2024). https://doi.org/10.46298/epiga.2024.10857.

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Анотація:
We partially extend to hyperk\"ahler fourfolds of Kummer type the results that we have proved regarding stable rigid vector bundles on hyperk\"ahler (HK) varieties of type $K3^{[n]}$. Let $(M,h)$ be a general polarized HK fourfold of Kummer type such that $q_M(h)\equiv -6\pmod{16}$ and the divisibility of $h$ is $2$, or $q_M(h)\equiv -6\pmod{144}$ and the divisibility of $h$ is $6$. We show that there exists a unique (up to isomorphism) slope stable vector bundle $\cal F$ on $M$ such that $r({\cal F})=4$, $ c_1({\cal F})=h$, $\Delta({\cal F})=c_2(M)$. Moreover $\cal F$ is rig
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14

Oberdieck, Georg. "Gromov–Witten theory and Noether–Lefschetz theory for holomorphic-symplectic varieties." Forum of Mathematics, Sigma 10 (2022). http://dx.doi.org/10.1017/fms.2022.10.

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Анотація:
Abstract We use Noether–Lefschetz theory to study the reduced Gromov–Witten invariants of a holomorphic-symplectic variety of $K3^{[n]}$ -type. This yields strong evidence for a new conjectural formula that expresses Gromov–Witten invariants of this geometry for arbitrary classes in terms of primitive classes. The formula generalizes an earlier conjecture by Pandharipande and the author for K3 surfaces. Using Gromov–Witten techniques, we also determine the generating series of Noether–Lefschetz numbers of a general pencil of Debarre–Voisin varieties. This reproves and extends a result of Debar
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15

Frei, Sarah, and Katrina Honigs. "Groups of symplectic involutions on symplectic varieties of Kummer type and their fixed loci." Forum of Mathematics, Sigma 11 (2023). http://dx.doi.org/10.1017/fms.2023.37.

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Анотація:
Abstract We describe the Galois action on the middle $\ell $ -adic cohomology of smooth, projective fourfolds $K_A(v)$ that occur as a fiber of the Albanese morphism on moduli spaces of sheaves on an abelian surface A with Mukai vector v. We show this action is determined by the action on $H^2_{\mathrm {\acute{e}t}}(A_{\bar {k}},{\mathbb Q}_{\ell }(1))$ and on a subgroup $G_A(v) \leqslant (A\times \hat {A})[3]$ , which depends on v. This generalizes the analysis carried out by Hassett and Tschinkel over ${\mathbb C}$ [21]. As a consequence, over number fields, we give a condition under which $
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16

Nesterov, Denis, and Georg Oberdieck. "Elliptic Curves in Hyper-Kähler Varieties." International Mathematics Research Notices, February 14, 2020. http://dx.doi.org/10.1093/imrn/rnaa016.

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Анотація:
Abstract We show that the moduli space of elliptic curves of minimal degree in a general Fano variety of lines of a cubic four-fold is a non-singular curve of genus $631$. The curve admits a natural involution with connected quotient. We find that the general Fano contains precisely $3,780$ elliptic curves of minimal degree with fixed (general) $j$-invariant. More generally, we express (modulo a transversality result) the enumerative count of elliptic curves of minimal degree in hyper-Kähler varieties with fixed $j$-invariant in terms of Gromov–Witten invariants. In $K3^{[2]}$-type this leads
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17

Bangere, Purnaprajna, Francisco Javier Gallego, and Miguel González. "Deformations of Hyperelliptic and Generalized Hyperelliptic Polarized Varieties." Mediterranean Journal of Mathematics 20, no. 2 (2023). http://dx.doi.org/10.1007/s00009-023-02278-5.

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Анотація:
AbstractThe purpose of this article is twofold. Firstly, we address and completely solve the following question: Let (X, L) be a smooth, hyperelliptic polarized variety and let $$\varphi : X \longrightarrow Y \subset \textbf{P}^N$$ φ : X ⟶ Y ⊂ P N be the morphism induced by |L|; when does $$\varphi $$ φ deform to a birational map? Secondly, we introduce the notion of “generalized hyperelliptic varieties” and carry out a study of their deformations. Regarding the first topic, we settle the non trivial, open cases of (X, L) being Fano-K3 and of (X, L) having dimension $$m \ge 2$$ m ≥ 2 , section
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18

Fatighenti, Enrico. "Examples of Non-Rigid, Modular Vector Bundles on Hyperkähler Manifolds." International Mathematics Research Notices, February 19, 2024. http://dx.doi.org/10.1093/imrn/rnae021.

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Анотація:
Abstract We exhibit examples of slope-stable and modular vector bundles on a hyperkähler manifold of K3$^{[2]}$-type, which move in a 20-dimensional family and study their algebraic properties. These are obtained by performing standard linear algebra constructions on the examples studied by O’Grady of (rigid) modular bundles on the Fano varieties of lines of a general cubic four-fold and the Debarre–Voisin hyperkähler manifold.
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19

Ascher, Kenneth, Kristin DeVleming, and Yuchen Liu. "Wall crossing for K‐moduli spaces of plane curves." Proceedings of the London Mathematical Society 128, no. 6 (2024). http://dx.doi.org/10.1112/plms.12615.

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Анотація:
AbstractWe construct proper good moduli spaces parametrizing K‐polystable ‐Gorenstein smoothable log Fano pairs , where is a Fano variety and is a rational multiple of the anticanonical divisor. We then establish a wall‐crossing framework of these K‐moduli spaces as varies. The main application in this paper is the case of plane curves of degree as boundary divisors of . In this case, we show that when the coefficient is small, the K‐moduli space of these pairs is isomorphic to the GIT moduli space. We then show that the first wall crossing of these K‐moduli spaces are weighted blow‐ups of Kir
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