Tautological algebra of the moduli space of semistable bundles on an elliptic curve

TL;DR

This paper investigates the algebraic relations among cohomology classes of Brill-Noether subvarieties in the moduli space of semistable bundles on an elliptic curve, drawing parallels to Poincaré relations.

Contribution

It establishes new relations among cohomology classes in the moduli space, extending known results from Jacobian varieties to elliptic curves.

Findings

Derived relations among cohomology classes of Brill-Noether subvarieties.

Established analogues of Poincaré relations for elliptic curves.

Enhanced understanding of the algebraic structure of the moduli space.

Abstract

In this paper, our aim is to find the relations amongst the cohomology classes of Brill-Noether subvarieties of the moduli space of semistable bundles over an elliptic curve. We obtain results similar to the Poincar\'e relations on a Jacobian variety.