A note on sheaves without self-extensions on the projective $n$-space

TL;DR

This paper proves that indecomposable rigid coherent sheaves on projective n-space have trivial endomorphism algebras, extending previous results known for the case n=2 to higher dimensions.

Contribution

The paper generalizes Drezet's result by showing that indecomposable rigid sheaves on projective n-space have trivial endomorphism algebras for all n.

Findings

Indecomposable rigid sheaves have trivial endomorphism algebras.

Extension of Drezet's result from n=2 to arbitrary n.

Provides insight into the structure of sheaves on projective spaces.

Abstract

Let ${\bf P}^n$ be the projective $n-$space over the complex numbers. In this note we show that an indecomposable rigid coherent sheaf on ${\bf P}^n$ has a trivial endomorphism algebra. This generalizes a result of Drezet for $n=2.$