On the Rationality of moduli spaces of vector bundles over chain-like curves

TL;DR

This paper studies the rationality of moduli spaces of semistable vector bundles over chain-like curves, focusing on arbitrary rank and fixed determinant, under certain Euler characteristic restrictions.

Contribution

It provides new results on the rationality of these moduli spaces for chain-like curves with specific Euler characteristic conditions.

Findings

Established rationality results for moduli spaces of vector bundles on chain-like curves.

Extended understanding of moduli space properties under Euler characteristic constraints.

Contributed to the classification of vector bundle moduli spaces over special algebraic curves.

Abstract

Let $C$ be a chain-like curve over $\mathbb{C}$. In this paper, we investigate the rationality of moduli spaces of $w$-semistable vector bundles on $C$ of arbitrary rank and fixed determinant by putting some restrictions on the Euler characteristics.