Globally generated vector bundles on complete intersection Calabi-Yau threefolds

TL;DR

This paper classifies and investigates globally generated vector bundles on complete intersection Calabi-Yau threefolds, focusing on cases with low first Chern class and specific ranks, advancing understanding of their structure.

Contribution

It provides a classification of globally generated vector bundles on quintic threefolds and studies rank 2 bundles on certain Calabi-Yau threefolds, offering new insights into their properties.

Findings

Complete classification of globally generated vector bundles on quintic threefolds.

Analysis of rank 2 bundles on codimension 2 Calabi-Yau threefolds.

Identification of conditions for global generation in these contexts.

Abstract

We investigate the globally generated vector bundles on complete intersection Calabi-Yau threefolds with the first Chern class at most 2. We classify all the globally generated vector bundles of an arbitrary rank on quintic in $\mathbb{P}^4$ and investigate the globally generated vector bundles of rank 2 on complete intersection Calabi-Yau threefolds of codimension 2.