On the Existence of Stable bundles with prescribed Chern classes on Calabi-Yau threefolds

TL;DR

This paper proves the existence of stable vector bundles with specific Chern classes on Calabi-Yau threefolds, advancing understanding in algebraic geometry and string theory compactifications.

Contribution

It establishes the existence of stable bundles with prescribed Chern classes on Calabi-Yau threefolds, confirming a case of a conjecture by Douglas, Reinbacher, and Yau.

Findings

Existence of certain stable vector bundle extensions over elliptically fibered Calabi-Yau threefolds

Verification of a case of the conjecture on stable bundles and Chern classes

Progress in understanding vector bundles on Calabi-Yau threefolds

Abstract

We prove a case of the conjecture of Douglas, Reinbacher and Yau about the existence of stable vector bundles with prescribed Chern classes on a Calabi-Yau threefold. For this purpose we prove the existence of certain stable vector bundle extensions over elliptically fibered Calabi-Yau threefolds.