GENERIC VANISHING THEORY VIA MIXED HODGE MODULES

DOI10.1017/fms.2013.1zbMath1281.14007arXiv1112.3058OpenAlexW2108446845MaRDI QIDQ2849813

Mihnea Popa, Christian Schnell

Publication date: 19 September 2013

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.3058

zbMATH Keywords

vanishing theorems\(D\)-modulesspecial sheavesBernstein-Sato ideals and polynomials

Mathematics Subject Classification ID

Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Vanishing theorems (32L20)

Related Items (15)

Fully faithful Fourier-Mukai functors and generic vanishing ⋮ Characteristic cycles and the microlocal geometry of the Gauss map, I ⋮ Vanishing theorems for perverse sheaves on abelian varieties, revisited ⋮ Cohomology jump loci of differential graded Lie algebras ⋮ Logarithmic comparison with smooth boundary divisor in mixed Hodge modules ⋮ On the Hopf problem and a conjecture of Liu-Maxim-Wang ⋮ Logarithmic Kodaira dimension and zeros of holomorphic log-one-forms ⋮ Kodaira dimension and zeros of holomorphic one-forms ⋮ Brody hyperbolicity of base spaces of certain families of varieties ⋮ Perverse sheaves on semi-abelian varieties ⋮ Hodge Ideals ⋮ Bernstein-Sato ideals and local systems ⋮ Holonomic \(D\)-modules on abelian varieties ⋮ Viehweg's hyperbolicity conjecture for families with maximal variation ⋮ Hodge modules on complex tori and generic vanishing for compact Kähler manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Modules de Hodge polarisables. (Polarisable Hodge modules)
• Strong generic vanishing and a higher-dimensional Castelnuovo-de Franchis inequality
• Derivative complex, BGG correspondence, and numerical inequalities for compact Kähler manifolds
• Local duality and polarized Hodge modules
• Kodaira dimension of irregular varieties
• Higher direct images of dualizing sheaves. II
• Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville
• Hodge theory with degenerating coefficients: \(L_2\) cohomology in the Poincaré metric
• Higgs bundles and local systems
• Canonical cohomology as an exterior module
• Sheaves with connection on abelian varieties
• Théorie de Hodge. II. (Hodge theory. II)
• Symmetric products of an algebraic curve
• GV-sheaves, Fourier-Mukai transform, and generic vanishing
• Deformations of the trivial line bundle and vanishing theorems
• Duality between D(X) and with its application to picard sheaves
• The Hodge theory of algebraic maps
• Differential Analysis on Complex Manifolds
• Higgs line bundles, Green-Lazarsfeld sets,\\and maps of K\"ahler manifolds to curves
• On the theory of mixed Hodge modules
• Subspaces of moduli spaces of rank one local systems
• Sheaf cohomology and free resolutions over exterior algebras
• The Geometry of Syzygies
• Singularities of theta divisors and the birational geometry of irregular varieties
• Mixed Hodge modules
• First order deformations for rank one local systems with a non-vanishing cohomology

This page was built for publication: GENERIC VANISHING THEORY VIA MIXED HODGE MODULES