Restriction theorems for semistable sheaves

TL;DR

This paper proves restriction theorems for semistable sheaves on smooth projective varieties, generalizing classical results and enabling the construction of higher-dimensional moduli spaces of sheaves.

Contribution

It extends restriction theorems to torsion-free sheaves with respect to the truncated Hilbert polynomial, broadening their applicability in algebraic geometry.

Findings

Established restriction theorems for (semi)stable sheaves

Generalized Mehta-Ramanathan restriction theorems

Constructed moduli spaces of sheaves in higher dimensions

Abstract

In this paper we prove restriction theorems for torsion-free sheaves that are (semi)stable with respect to the truncated Hilbert polynomial over a smooth projective variety. Our results apply in particular to Gieseker-semistable sheaves and generalize the well-known restriction theorems of Mehta and Ramanathan. As an application we construct a moduli space of sheaves in higher dimensions.