On a conjecture of Kazhdan and Polishchuk

TL;DR

This paper examines a conjecture related to a specific variety associated with stable rank 2 vector bundles of degree 2g-1 on smooth projective complex curves, aiming to understand its properties and implications.

Contribution

It provides an analysis and potential proof or insights into a conjecture connecting stable vector bundles and associated varieties, advancing understanding in algebraic geometry.

Findings

Insights into the structure of the variety linked to stable vector bundles

Progress towards proving or understanding Kazhdan and Polishchuk's conjecture

Potential new methods for studying vector bundles on algebraic curves

Abstract

We discuss a conjecture made by Alexander Polishchuk and David Kazhdan at the 2022 ICM about a variety naturally attached to any stable vector bundle of rank 2 and degree $2g- 1$ on a smooth projective complex curve of genus $g$.