The local cohomology of the Jacobian ring

zbMath1314.14089arXiv1306.3736MaRDI QIDQ462464

Edoardo Sernesi

Publication date: 20 October 2014

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.3736

zbMATH Keywords

Hodge decompositionhypersurfaceslocal cohomologyarrangements of hyperplanesJacobian idealstable vector bundlesfree divisorslogarithmic differential formslogarithmic vector fieldsMacaulay's theoremTorelli type theorems

Mathematics Subject Classification ID

Local cohomology and algebraic geometry (14B15) Hypersurfaces and algebraic geometry (14J70) Local complex singularities (32S05) Mixed Hodge theory of singular varieties (complex-analytic aspects) (32S35) Torelli problem (14C34)

Related Items (23)

Logarithmic vector fields and freeness of divisors and arrangements: new perspectives and applications. Abstracts from the workshop held January 24--30, 2021 (online meeting) ⋮ Jacobian syzygies, fitting ideals, and plane curves with maximal global Tjurina numbers ⋮ Quasi-complete intersections in \(\mathbb{P}^2\) and syzygies ⋮ Splitting types of bundles of logarithmic vector fields along plane curves ⋮ On the jumping lines of bundles of logarithmic vector fields along plane curves ⋮ Freeness versus maximal global Tjurina number for plane curves ⋮ Projective rigidity and Alexander polynomials of certain nodal hypersurfaces ⋮ On the Hilbert vector of the Jacobian module of a plane curve ⋮ Numerical invariants and moduli spaces for line arrangements ⋮ Computing Milnor fiber monodromy for some projective hypersurfaces ⋮ Syzygies and logarithmic vector fields along plane curves ⋮ The Hessian polynomial and the Jacobian ideal of a reduced hypersurface in \(\mathbb{P}^n\) ⋮ Self-duality of the local cohomology of the Jacobian ring and Gherardelli's theorem ⋮ The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds ⋮ On rational cuspidal plane curves and the local cohomology of Jacobian rings ⋮ Saturation of Jacobian ideals: some applications to nearly free curves, line arrangements and rational cuspidal plane curves ⋮ Plane curves with three syzygies, minimal Tjurina curves, and nearly cuspidal curves ⋮ Higher order Jacobians, Hessians and Milnor algebras ⋮ Duality and socle generators for residual intersections ⋮ Line and rational curve arrangements, and Walther's inequality ⋮ Versality, Bounds of Global Tjurina Numbers and Logarithmic Vector Fields Along Hypersurfaces with Isolated Singularities ⋮ Addition-deletion results for the minimal degree of a Jacobian syzygy of a union of two curves ⋮ On Some Conjectures About Free and Nearly Free Divisors

Uses Software

• Macaulay2

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