A generalization of Griffiths's theorem on rational integrals

DOI10.1215/S0012-7094-06-13523-8zbMath1117.14012arXivmath/0501253OpenAlexW1971186411MaRDI QIDQ854578

Morihiko Saito, Alexandru Dimca

Publication date: 5 December 2006

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0501253

zbMATH Keywords

Hodge filtrationrational singularitiesKodaira-Spencer mapGauss-Manin connectionprojective hypersurfacesJacobian ringspectral numbers\(\mathbb Q\)-manifoldspole-order filtrationsemi-weighted homogeneous isolated singularities

Mathematics Subject Classification ID

de Rham cohomology and algebraic geometry (14F40) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Hypersurfaces and algebraic geometry (14J70) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40) Mixed Hodge theory of singular varieties (complex-analytic aspects) (32S35)

Related Items

A generalization of Griffiths' theorem on rational integrals. II, Hodge ideals and spectrum of isolated hypersurface singularities, On the torsion of Brieskorn modules of homogeneous polynomials, Feynman integrals and motives of configuration spaces, On the syzygies and Alexander polynomials of nodal hypersurfaces, Chebyshev curves, free resolutions and rational curve arrangements, Jumping coefficients and spectrum of a hyperplane arrangement, Computing periods of rational integrals, Bernstein-Sato polynomials of hyperplane arrangements, Higher order Jacobians, Hessians and Milnor algebras, Koszul Complexes and Pole Order Filtrations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some local consequences of Hodge theory
• On the mixed Hodge structure on the cohomology of the Milnor fibre
• Intersection homology theory
• Singularities and topology of hypersurfaces
• B-functions and holonomic systems. Rationality of roots of B-functions
• On deformations of compactifiable complex manifolds
• On \(b\)-function, spectrum and rational singularity
• Hodge numbers of hypersurfaces
• Local contributions to global deformations of surfaces
• Die Auflösung der rationalen Singularitäten holomorpher Abbildungen
• Monodromy of isolated singularities of hypersurfaces
• Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen
• On the periods of certain rational integrals. I, II
• Equations différentielles à points singuliers réguliers
• Variation of mixed Hodge structures arising from family of logarithmic deformations
• Filtrations de Hodge et par l'ordre du pôle pour les hypersurfaces singulières
• On microlocal $b$-function
• Koszul Complexes and Hypersurface Singularities
• Multiplier ideals, 𝑉-filtration, and spectrum
• Brieskorn modules and Gauss-Manin systems for non-isolated hypersurface singularities
• Singularities of theta divisors and the birational geometry of irregular varieties
• Mixed Hodge modules