Konstantia Manousou Sotiropoulou

NKUA

Equivariant Koszul Cohomology of Canonical Curves

This poster studies the representation-theoretic structure of the Koszul cohomology of a smooth projective variety $X$ over an algebraically closed field $k$, endowed with an action of a finite group $G$ whose order is coprime to $\text{char}(k)$. Using properties of $G$-equivariant functors, we show that the associated Koszul complex naturally carries a $G$-module structure, and we extend classical dimension formulas to identities of virtual representations. For canonical curves, these results become explicit through equivariant Euler characteristics, equivariant Riemann–Roch, and generating functions for Schur functors.