Hodge Ideals

DOI10.1090/memo/1268zbMath1442.14004arXiv1605.08088OpenAlexW3037389875MaRDI QIDQ5213181

Mihnea Popa, Mircea Mustaţă

Publication date: 31 January 2020

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.08088

zbMATH Keywords

Kodaira vanishing theoremHodge filtrationde Rham complexPrym varieties\(D\)-modulestheta divisors\(b\)-functionlogarithmic differential formsample divisorsHodge modulessimple normal crossing divisorspole order filtrationpolarized abelian varietiescomplements of hypersurfacesNadel vanishing theoremvanishing criteriaAkizuki-Nakano vanishing theoremArtin vanishing theoremgeneric determinantal hypersurfacesGriffiths vanishing theoremsemiquasihomogeneous isolated singularities

Mathematics Subject Classification ID

Vanishing theorems in algebraic geometry (14F17) Singularities of surfaces or higher-dimensional varieties (14J17) Sheaves of differential operators and their modules, (D)-modules (32C38) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Variation of Hodge structures (algebro-geometric aspects) (14D07) Complex surface and hypersurface singularities (32S25) Multiplier ideals (14F18)

Related Items

Hodge filtration on local cohomology, Du Bois complex and local cohomological dimension ⋮ Bernstein–Sato functional equations, V-filtrations, and multiplier ideals of direct summands ⋮ Hodge ideals of free divisors ⋮ Hodge ideals and spectrum of isolated hypersurface singularities ⋮ The Du Bois complex of a hypersurface and the minimal exponent ⋮ ON A BERNSTEIN–SATO POLYNOMIAL OF A MEROMORPHIC FUNCTION ⋮ Higher Du Bois singularities of hypersurfaces ⋮ Hodge modules and singular Hermitian metrics ⋮ An algorithm for Hodge ideals ⋮ The higher Du Bois and higher rational properties for isolated singularities ⋮ HODGE IDEALS FOR -DIVISORS, -FILTRATION, AND MINIMAL EXPONENT ⋮ Differential operators, retracts, and toric face rings ⋮ Weighted Hodge ideals of reduced divisors ⋮ Hodge ideals for the determinant hypersurface ⋮ Hodge filtration, minimal exponent, and local vanishing ⋮ ON THE MILNOR MONODROMY OF THE IRREDUCIBLE COMPLEX REFLECTION ARRANGEMENTS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kodaira-Saito vanishing and applications
• Modules de Hodge polarisables. (Polarisable Hodge modules)
• A numerical criterion for very ample line bundles
• On Saito's vanishing theorem
• A generalization of Griffiths' theorem on rational integrals. II
• A remark on hypersurfaces with isolated singularities
• \(D\)-modules, perverse sheaves, and representation theory. Translated from the Japanese by Kiyoshi Takeuchi
• Andreotti-Mayer loci and the Schottky problem
• Cubic threefolds and abelian varieties of dimension five. II
• On the structure of Brieskorn lattice
• Vector bundles on complex projective spaces
• On the theory of b-functions
• On \(b\)-function, spectrum and rational singularity
• Sheaves in topology
• Bounds for log canonical thresholds with applications to birational rigidity
• The degree of the Gauss map of the theta divisor
• On the syzygies and Hodge theory of nodal hypersurfaces
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Troisième partie). Rédigé avec la colloboration de J. Dieudonné
• Equations différentielles à points singuliers réguliers
• Sul massimo numero di nodi di una superficie di dato ordine dello spazio ordinario o di una forma di un iperspazio
• GENERIC VANISHING THEORY VIA MIXED HODGE MODULES
• Introduction to Toric Varieties. (AM-131)
• Filtrations de Hodge et par l'ordre du pôle pour les hypersurfaces singulières
• Singularities of Pairs
• A young person's guide to mixed Hodge modules
• Restriction, Subadditivity, and Semicontinuity Theorems for Hodge Ideals
• On the syzygies and Alexander polynomials of nodal hypersurfaces
• Positivity for Hodge modules and geometric applications
• Koszul Complexes and Pole Order Filtrations
• Singularities of theta divisors and the birational geometry of irregular varieties
• Mixed Hodge modules
• On smooth Gorenstein polytopes