The Period-Index Problem of the Canonical Gerbe of Symplectic and Orthogonal Bundles

TL;DR

This paper investigates the period and index of the canonical gerbe associated with stable parabolic symplectic and orthogonal bundles over algebraic curves, addressing a key problem in algebraic geometry.

Contribution

It provides a solution to the period-index problem for the canonical gerbe of these bundles, advancing understanding of their moduli spaces.

Findings

Determined the period and index of the gerbe for these bundles.

Established the relationship between the gerbe's period and index.

Solved the period-index problem in this geometric context.

Abstract

We consider regularly stable parabolic symplectic and orthogonal bundles over an irreducible smooth projective curve over an algebraically closed field of characteristic zero. The morphism from the moduli stack of such bundles to its coarse moduli space is a $\mu_2$-gerbe. We study the period and index of this gerbe, and solve the corresponding period-index problem.