Syzygies in Hilbert schemes of complete intersections

DOI10.1016/j.jalgebra.2022.12.015OpenAlexW2922744606MaRDI QIDQ2682827

Alessio Sammartano, Giulio Caviglia

Publication date: 1 February 2023

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

Full work available at URL: https://arxiv.org/abs/1903.08770

zbMATH Keywords

Betti numbersEisenbud-Green-Harris conjectureLex-plus-powers conjecturestrongly stable idealClements-Lindström ringfinite subschemeinfinite free resolutions

Mathematics Subject Classification ID

Linkage, complete intersections and determinantal ideals (13C40) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Parametrization (Chow and Hilbert schemes) (14C05) Syzygies, resolutions, complexes and commutative rings (13D02)

Uses Software

• Macaulay2

Cites Work

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• Sharp upper bounds for the Betti numbers of a given Hilbert polynomial
• The Lex-Plus-Powers conjecture holds for pure powers
• Segments and Hilbert schemes of points
• Minimal free resolutions over complete intersections
• The number of generators of a colength N ideal in a power series ring
• Dimension of the punctual Hilbert scheme
• Componentwise linear ideals and Golod rings
• On the Lex-plus-powers conjecture
• Resolutions of \textbf{a}-stable ideals.
• The Eisenbud-Green-Harris conjecture for defect two quadratic ideals
• Strongly stable ideals and Hilbert polynomials
• Borel-plus-powers monomial ideals
• Layered resolutions of Cohen-Macaulay modules
• Graded Betti numbers of balanced simplicial complexes
• On the growth of deviations
• Hilbert schemes and Betti numbers over Clements–Lindström rings
• Algorithms for strongly stable ideals
• Number of generators of ideals
• Hyperplane arrangement cohomology and monomials in the exterior algebra
• Resolutions of monomial ideals and cohomology over exterior algebras
• The Eisenbud-Green-Harris Conjecture
• A generalization of a combinatorial theorem of macaulay

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