The Chow ring of the moduli space and its related homogeneous space of bundles on P^2 with charge 1

TL;DR

This paper computes the Chow ring of a specific moduli space of SO(n,K)-bundles on the projective plane with fixed topological and trivialization conditions, advancing understanding of algebraic cycles in these moduli spaces.

Contribution

It explicitly determines the Chow ring structure for a class of bundles on P^2 with specified topological charge and trivialization, a novel calculation in algebraic geometry.

Findings

Chow ring of the moduli space is explicitly described.

Results hold over algebraically closed fields with characteristic not equal to 2.

Provides new insights into the intersection theory of bundle moduli spaces.

Abstract

For an algebraically closed field K with ch K \not = 2, we determine the Chow ring of the moduli space of holomorphic bundles on a projective plane with the structure group SO(n,K) and half the first Pontryagin index being equal to 1, each of which is trivial on a fixed line and has a fixed holomorphic trivialization there.