Equivariant Koszul Cohomology of Canonical Curves

2025/12/22 by Kostas Karagiannis, Aristides Kontogeorgis, Karagiannis, Kostas +3
Mathematics · #14H37 (Primary) 13D02 14F43 20C15 14C40 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.19894

openalex publication_date 2025/12/22 · openalex created_date 2025/12/25 · openalex updated_date 2026/07/28

Abstract

This paper investigates the representation-theoretic structure of the Koszul cohomology of a smooth projective variety X over an algebraically closed field k, admitting an action of a finite group G of order coprime to \rm char(k). Properties of G-equivariant functors are employed to show that the associated Koszul complex is a complex of kG-modules, and to generalize known dimension formulas to identities between virtual representations. In the case of canonical curves, explicit formulas are obtained by combining the theory of equivariant Euler characteristics and equivariant Riemann-Roch theorems with that of generating functions for Schur functors.

Citations

• Progress on syzygies of algebraic curves
• Integral representations of cyclic groups acting on relative holomorphic differentials of deformations of curves with automorphisms
• Computing the equivariant Euler characteristic of Zariski and etale sheaves on curves
• Ueber die Theorie der algebraischen Formen

Related

• Computing the homology of Koszul complexes
• Relative homological algebra, equivariant de Rham theory, and Koszul duality
• Koszul modules with vanishing resonance in algebraic geometry
• Equivariant Koszul Duality, Modular Category O, and Periodic Kazhdan--Lusztig Polynomials
• An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson