Cohomological vanishing on blown-up projective spaces

TL;DR

This paper proves precise cohomological vanishing results for line bundles on blow-ups of projective space at up to n+1 points using elementary toric geometry techniques.

Contribution

It introduces new sharp vanishing theorems for line bundles on blown-up projective spaces with minimal point configurations.

Findings

Established sharp cohomological vanishing conditions

Applied elementary toric geometry techniques

Focused on blow-ups at no more than n+1 points

Abstract

By utilizing elementary techniques from toric geometry, we prove sharp cohomological vanishing results for line bundles defined on the blow-up of projective space $\mathbb{P}^n$ at no more than $n+1$ points.