Weakly uniform rank two vector bundles on multiprojective spaces

TL;DR

This paper classifies weakly uniform rank two vector bundles on multiprojective spaces and proves triviality or splitting results for higher-rank bundles with specific splitting types.

Contribution

It provides a classification of weakly uniform rank two bundles and establishes triviality or splitting criteria for higher-rank bundles with certain splitting types.

Findings

Classified weakly uniform rank two vector bundles on multiprojective spaces.

Proved higher-rank weakly uniform bundles with zero splitting type are trivial.

Showed higher-rank uniform bundles with decreasing splitting types split.

Abstract

Here we classify the weakly uniform rank two vector bundles on multiprojective spaces. Moreover we show that every rank $r>2$ weakly uniform vector bundle with splitting type $a_{1,1}=...=a_{r,s}=0$ is trivial and every rank $r>2$ uniform vector bundle with splitting type $a_1>...>a_r$, splits.