The first cohomology of separably rationally connected varieties

TL;DR

This paper proves that for separably rationally connected varieties over algebraically closed fields of positive characteristic, the first cohomology group of the structure sheaf vanishes, revealing a key geometric property.

Contribution

It establishes the vanishing of H^1(X, O_X) for separably rationally connected varieties in positive characteristic, a result previously unknown.

Findings

H^1(X, O_X)=0 for separably rationally connected varieties

Provides insight into the structure of such varieties in positive characteristic

Advances understanding of cohomological properties in algebraic geometry

Abstract

In this short note we prove that if X is a separably rationally connected variety over an algebraically closed field of positive characteristic, then H^1(X, O_X)=0.