Some rational subvarieties of moduli spaces of stable vector bundles

TL;DR

This paper constructs special subvarieties within moduli spaces of stable vector bundles on complex projective varieties, using Grassmannian parametrizations to explore their structure.

Contribution

It introduces a method to generate families of stable vector bundles with fixed determinant and rank, parametrized by Grassmannians, revealing new subvarieties in moduli spaces.

Findings

Constructed families of stable vector bundles with fixed determinant and rank

Identified subvarieties in moduli spaces birational to Grassmannians

Provided explicit parametrizations using Grassmannian varieties

Abstract

Let X be a smooth complex irreducible projective variety of dimension $n \geq 2$ and $H$ be an ample line bundle on $X$. In this paper, we construct families of $\mu_H$-stable vector bundles on $X$ having fixed determinant and rank $r$, which are generated by $r+1$ global sections, parametrized by Grassmanian varieties. This gives into the corresponding moduli spaces special subvarieties birational to Grassmannian.