Relevant bibliographies by topics / Tautological bundle

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Tautological bundle'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Tautological bundle"

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BISWAS, INDRANIL, and FATIMA LAYTIMI. "PARABOLIC k-AMPLE BUNDLES." International Journal of Mathematics 22, no. 11 (2011): 1647–60. http://dx.doi.org/10.1142/s0129167x11007367.

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We construct projectivization of a parabolic vector bundle and a tautological line bundle over it. It is shown that a parabolic vector bundle is ample if and only if the tautological line bundle is ample. This allows us to generalize the notion of a k-ample bundle, introduced by Sommese, to the context of parabolic bundles. A parabolic vector bundle E* is defined to be k-ample if the tautological line bundle [Formula: see text] is k-ample. We establish some properties of parabolic k-ample bundles.
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D'souza, Harry. "On a spanned tautological bundle." MATHEMATICA SCANDINAVICA 67 (June 1, 1990): 56. http://dx.doi.org/10.7146/math.scand.a-12319.

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Ananyevskiy, Alexey. "The special linear version of the projective bundle theorem." Compositio Mathematica 151, no. 3 (2014): 461–501. http://dx.doi.org/10.1112/s0010437x14007702.

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AbstractA special linear Grassmann variety $\text{SGr}(k,n)$ is the complement to the zero section of the determinant of the tautological vector bundle over $\text{Gr}(k,n)$. For an $SL$-oriented representable ring cohomology theory $A^{\ast }(-)$ with invertible stable Hopf map ${\it\eta}$, including Witt groups and $\text{MSL}_{{\it\eta}}^{\ast ,\ast }$, we have $A^{\ast }(\text{SGr}(2,2n+1))\cong A^{\ast }(pt)[e]/(e^{2n})$, and $A^{\ast }(\text{SGr}(k,n))$ is a truncated polynomial algebra over $A^{\ast }(pt)$ whenever $k(n-k)$ is even. A splitting principle for such theories is established
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Marian, Alina, Dragos Oprea, Rahul Pandharipande, Aaron Pixton та Dimitri Zvonkine. "The Chern character of the Verlinde bundle over ℳ¯ g,n". Journal für die reine und angewandte Mathematik (Crelles Journal) 2017, № 732 (2017): 147–63. http://dx.doi.org/10.1515/crelle-2015-0003.

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Abstract We prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over \overline{\mathcal{M}}_{g,n} in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the ranks, given by the Verlinde formula, determine a semisimple fusion algebra). According to Teleman’s classification of semisimple CohFTs, there exists an element of Givental’s group transforming the fusion algebra into the CohFT. We determine the element using the first Chern class of the Verlinde bundle on the interior {\mathcal{M}}_{g,n} and
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Biswas, Indranil, and A. J. Parameswaran. "Monodromy group for a strongly semistable principal bundle over a curve, II." Journal of K-theory 1, no. 3 (2008): 583–607. http://dx.doi.org/10.1017/is007011017jkt015.

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AbstractLet X be a geometrically irreducible smooth projective curve defined over a field k. Assume that X has a k–rational point; fix a k–rational point x ε X. From these data we construct an affine group scheme X defined over the field k as well as a principal X–bundle over the curve X. The group scheme X is given by a ℚ–graded neutral Tannakian category built out of all strongly semistable vector bundles over X. The principal bundle is tautological. Let G be a linear algebraic group, defined over k, that does not admit any nontrivial character which is trivial on the connected component, co
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Boissière, Samuel, and Marc A. Nieper-Wisskirchen. "Generating Series in the Cohomology of Hilbert Schemes of Points on Surfaces." LMS Journal of Computation and Mathematics 10 (2007): 254–70. http://dx.doi.org/10.1112/s146115700000139x.

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In the study of the rational cohomology of Hilbert schemes of points on a smooth surface, it is particularly interesting to understand the characteristic classes of the tautological bundles and the tangent bundle. In this note we pursue this study. We first collect all results appearing separately in the literature and prove some new formulas using Ohmoto's results on orbifold Chern classes on Hilbert schemes. We also explain the algorithmic counterpart of the topic: the cohomology space is governed by a vertex algebra that can be used to compute characteristic classes. We present an implement
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Wandel, Malte. "Stability of tautological bundles on the Hilbert scheme of two points on a surface." Nagoya Mathematical Journal 214 (June 2014): 79–94. http://dx.doi.org/10.1017/s0027763000010850.

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AbstractLet (X, H) be a polarized smooth projective surface satisfyingH1(Χ, OΧ) = 0, and letƑbe either a rank 1 torsion-free sheaf or a rank 2μH-stable vector bundle onΧ. Assume thatc1(Ƒ) ≠ 0. This article shows that the rank 2—respectively, rank 4—tautological sheafƑ[2]associated withƑon the Hilbert squareΧ[2]isμ-stable with respect to a certain polarization.
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Wandel, Malte. "Stability of tautological bundles on the Hilbert scheme of two points on a surface." Nagoya Mathematical Journal 214 (June 2014): 79–94. http://dx.doi.org/10.1215/00277630-2416410.

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AbstractLet (X, H) be a polarized smooth projective surface satisfyingH1(Χ, OΧ) = 0, and letƑbe either a rank 1 torsion-free sheaf or a rank 2μH-stable vector bundle onΧ. Assume thatc1(Ƒ) ≠ 0. This article shows that the rank 2—respectively, rank 4—tautological sheafƑ[2]associated withƑon the Hilbert squareΧ[2]isμ-stable with respect to a certain polarization.
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Bérczi, Gergely. "Thom Polynomials and the Green–Griffiths–Lang Conjecture for Hypersurfaces with Polynomial Degree." International Mathematics Research Notices 2019, no. 22 (2017): 7037–92. http://dx.doi.org/10.1093/imrn/rnx332.

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Abstract Green and Griffiths [25] and Lang [29] conjectured that for every complex projective algebraic variety X of general type there exists a proper algebraic subvariety of X containing all nonconstant entire holomorphic curves $f:{\mathbb{C}} \to X$. We construct a compactification of the invariant jet differentials bundle over complex manifolds motivated by an algebraic model of Morin singularities and we develop an iterated residue formula using equivariant localisation for tautological integrals over it. Using this we show that the polynomial Green–Griffiths–Lang conjecture for a generi
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Goldring, Wushi. "The Griffiths bundle is generated by groups." Mathematische Annalen 375, no. 3-4 (2019): 1283–305. http://dx.doi.org/10.1007/s00208-019-01899-0.

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Abstract First the Griffiths line bundle of a $$\mathbf {Q}$$ Q -VHS $${\mathscr {V}}$$ V is generalized to a Griffiths character $${{\,\mathrm{grif}\,}}(\mathbf {G}, \mu ,r)$$ grif ( G , μ , r ) associated to any triple $$(\mathbf {G}, \mu , r)$$ ( G , μ , r ) , where $$\mathbf {G}$$ G is a connected reductive group over an arbitrary field F, $$\mu \in X_*(\mathbf {G})$$ μ ∈ X ∗ ( G ) is a cocharacter (over $$\overline{F}$$ F ¯ ) and $$r:\mathbf {G}\rightarrow GL(V)$$ r : G → G L ( V ) is an F-representation; the classical bundle studied by Griffiths is recovered by taking $$F=\mathbf {Q}$$ F
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Dissertations / Theses on the topic "Tautological bundle"

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Wandel, Malte [Verfasser]. "Stability of tautological bundles on Hilbert schemes of points on a surface / Malte Wandel." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2013. http://d-nb.info/1043723609/34.

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Galeotti, Mattia Francesco. "Moduli of curves with principal and spin bundles : singularities and global geometry." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066485/document.

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L'espace de modules Mgbar des courbes stables de genre g est un object central en géométrie algébrique. Du point de vue de la géométrie birationelle, il apparaît naturel se demander si Mgbar est de type générale. Harris-Mumford et Eisenbud-Harris ont montré que Mgbar est de type générale pour un genre g>=24 et g=22. Le cas g=23 est encore misterieux. Dans les dix dernières années une nouvelle approche a émergé, dans l'essai de clarifier ça : l'idée est celle de considérer de recouvrement fini de Mgbar qui sont des espaces de modules de courbes stables munies d'une structure additionnelle co
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Scala, Luca. "Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles : perturbations of the metric in Seiberg-Witten equations." Paris 7, 2005. http://www.theses.fr/2005PA077185.

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Meth, John Charles. "Rational embeddings of the Severi Brauer variety." Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-05-916.

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In an attempt to prove Amitsur's Conjecture for cyclic subgroups of the Brauer group, we look at rational embeddings of the Severi Brauer variety of an algebra into its norm hypersurface. We enlarge the collection of such embeddings, and generalize them to embeddings of generalized Severi Brauer varieties into determinantal varieties.<br>text
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Book chapters on the topic "Tautological bundle"

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Abate, Marco. "Index theorems for meromorphic self-maps of the projective space." In Frontiers in Complex Dynamics, edited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691159294.003.0017.

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This chapter uses techniques from the theory of local dynamics of holomorphic germs tangent to the identity to prove three index theorems for global meromorphic maps of projective space. More precisely, the chapter seeks to prove a particular index theorem: Let f : ℙⁿ ⇢ ℙⁿ be a meromorphic self-map of degree ν‎ + 1 ≥ 2 of the complex n-dimensional projective space. Let Σ‎(f) = Fix(f) ∪ I(f) be the union of the indeterminacy set I(f) of f and the fixed points set Fix(f) of f. Let Σ‎(f) = ⊔subscript Greek Small Letter AlphaΣ‎subscript Greek Small Letter Alpha be the decomposition of Σ‎ in connected components, and denote by N the tautological line bundle of ℙⁿ. After laying out the statements under this theorem, the chapter discusses the proofs.
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