Stability and cohomology of kernel bundles on projective space

TL;DR

This paper investigates the cohomology, stability, and ampleness of kernel bundles on projective space, providing asymptotic vanishing results and criteria for stability and ampleness.

Contribution

It offers new asymptotic cohomology vanishing theorems and characterizations of stability and ampleness for Steiner bundles on projective space.

Findings

Proved an asymptotic cohomology vanishing theorem.

Characterized the stability of general Steiner bundles.

Provided a criterion for Steiner bundles to be ample.

Abstract

In this paper, we study the cohomology of vector bundles on projective space defined as kernels or cokernels of general maps $V_1 \to V_2$, where the $V_i$ are direct sums of line bundles or certain exceptional bundles. We prove an asymptotic cohomology vanishing theorem. We characterize the stability of general Steiner bundles on projective space. We also give a criterion for a Steiner bundle to be ample.