Hilbert Series and Lefschetz Properties of Dimension One Almost Complete Intersections

DOI10.1080/00927872.2015.1087535zbMath1439.13041arXiv1403.5921OpenAlexW2964218043MaRDI QIDQ2817522

Alexandru Dimca, Dorin Popescu

Publication date: 31 August 2016

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5921

zbMATH Keywords

isolated singularitiesprojective hypersurfacesLefschetz propertyalmost complete intersections

Mathematics Subject Classification ID

Linkage, complete intersections and determinantal ideals (13C40) Singularities in algebraic geometry (14B05) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Divisors, linear systems, invertible sheaves (14C20)

Related Items (11)

Jacobian syzygies, fitting ideals, and plane curves with maximal global Tjurina numbers ⋮ 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 ⋮ On the minimal value of global Tjurina numbers for line arrangements ⋮ On the Hilbert vector of the Jacobian module of a plane curve ⋮ 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 ⋮ Line and rational curve arrangements, and Walther's inequality

Cites Work

• New free divisors from old
• Syzygies and logarithmic vector fields along plane curves
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• Homology of homogeneous divisors
• Cayley-Bacharach theorems and conjectures
• On the syzygies and Alexander polynomials of nodal hypersurfaces
• Koszul Complexes and Pole Order Filtrations
• Gorenstein-duality for one-dimensional almost complete intersections-with an application to non-isolated real singularities

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