Results 1 to 10 of about 365 (63)
Finite $F$-representation type for homogeneous coordinate rings of non-Fano varieties [PDF]
Épijournal de Géométrie Algébrique, 2023 Finite $F$-representation type is an important notion in characteristic-$p$ commutative algebra, but explicit examples of varieties with or without this property are few.
Devlin Mallory
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Weighted Hodge ideals of reduced divisors
Forum of Mathematics, Sigma, 2023 We study the Hodge and weight filtrations on the localization along a hypersurface, using methods from birational geometry and the V-filtration induced by a local defining equation.
Sebastián Olano
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Hodge filtration on local cohomology, Du Bois complex and local cohomological dimension
Forum of Mathematics, Pi, 2022 We study the Hodge filtration on the local cohomology sheaves of a smooth complex algebraic variety along a closed subscheme Z in terms of log resolutions and derive applications regarding the local cohomological dimension, the Du Bois complex, local ...
Mircea Mustaţă, Mihnea Popa
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Log $\mathscr{D}$-modules and index theorems
Forum of Mathematics, Sigma, 2021 We study log $\mathscr {D}$-modules on smooth log pairs and construct a comparison theorem of log de Rham complexes. The proof uses Sabbah’s generalized b-functions.
Lei Wu, Peng Zhou
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Abundance for varieties with many differential forms [PDF]
Épijournal de Géométrie Algébrique, 2018 We prove that the abundance conjecture holds on a variety $X$ with mild singularities if $X$ has many reflexive differential forms with coefficients in pluricanonical bundles, assuming the Minimal Model Program in lower dimensions.
Vladimir Lazić, Thomas Peternell
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HODGE IDEALS FOR $\mathbb{Q}$-DIVISORS, $V$-FILTRATION, AND MINIMAL EXPONENT
Forum of Mathematics, Sigma, 2020 We compute the Hodge ideals of $\mathbb{Q}$-divisors in terms of the $V$-filtration induced by a local defining equation, inspired by a result of Saito in the reduced case. We deduce basic properties of Hodge ideals in this generality, and relate them to
MIRCEA MUSTAŢĂ, MIHNEA POPA
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Equivariant perverse sheaves on Coxeter arrangements and buildings [PDF]
Épijournal de Géométrie Algébrique, 2019 When $W$ is a finite Coxeter group acting by its reflection representation on $E$, we describe the category ${\mathsf{Perv}}_W(E_{\mathbb C}, {\mathcal{H}}_{\mathbb C})$ of $W$-equivariant perverse sheaves on $E_{\mathbb C}$, smooth with respect to the ...
Martin H. Weissman
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The Bernstein-Sato b-Function of the Space of Cyclic Pairs [PDF]
, 2015 We compute the Bernstein-Sato polynomial of $f$, a function which given a pair $(M,v)$ in $X = M_n(\mathbf{C}) \times \mathbf{C}^n$ tests whether $v$ is a cyclic vector for $M$.
Walters, Robin
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Differential operators and flat connections on a Riemann surface
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 64, Page 4041-4056, 2003., 2003 We consider filtered holomorphic vector bundles on a compact Riemann surface X equipped with a holomorphic connection satisfying a certain transversality condition with respect to the filtration. If Q is a stable vector bundle of rank r and degree (1 − genus(X))nr, then any holomorphic connection on the jet bundle Jn(Q) satisfies this transversality ...
Indranil Biswas
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GENERIC VANISHING THEORY VIA MIXED HODGE MODULES
Forum of Mathematics, Sigma, 2013 We extend most of the results of generic vanishing theory to bundles of holomorphic forms and rank-one local systems, and more generally to certain coherent sheaves of Hodge-theoretic origin associated with irregular varieties. Our main tools are Saito’s
MIHNEA POPA, CHRISTIAN SCHNELL
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