The Hilbert-Kunz functions of two-dimensional rings of type ADE

DOI10.1016/j.jalgebra.2016.09.004zbMath1360.13016arXiv1308.5085OpenAlexW2963715959MaRDI QIDQ330170

Daniel Brinkmann

Publication date: 24 October 2016

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

Full work available at URL: https://arxiv.org/abs/1308.5085

zbMATH Keywords

vector bundleFrobeniusmatrix factorizationmaximal Cohen-MacaulayHilbert-Kunz functionHilbert-seriesSyzygy moduleADE singularity

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Representation theory for linear algebraic groups (20G05) Singularities of surfaces or higher-dimensional varieties (14J17) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Actions of groups on commutative rings; invariant theory (13A50) Syzygies, resolutions, complexes and commutative rings (13D02) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Cohen-Macaulay modules (13C14)

Related Items (1)

F-signature function of quotient singularities

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The rationality of the Hilbert-Kunz multiplicity in graded dimension two
• Matrix factorizations and representations of quivers. II: Type \(ADE\) case.
• Some surprising Hilbert-Kunz functions
• Hilbert-Kunz multiplicity and an inequality between multiplicity and colength
• Frobenius splitting methods in geometry and representation theory
• Semistability and Hilbert-Kunz multiplicities for curves
• Cohen-Macaulay modules on hypersurface singularities. I
• Cohen-Macaulay modules on hypersurface singularities. II
• The Hilbert-Kunz function
• Two theorems about maximal Cohen-Macaulay modules
• Mason's theorem and syzygy gaps
• Rationale Singularitäten komplexer Flächen
• Maximal Cohen-Macaulay modules over surface singularities
• Homological Algebra on a Complete Intersection, with an Application to Group Representations
• On Noetherian Rings of Characteristic p
• The Hilbert–Kunz Function in Graded Dimension Two
• On a Problem of Miyaoka
• On Isolated Rational Singularities of Surfaces

This page was built for publication: The Hilbert-Kunz functions of two-dimensional rings of type ADE