On the moduli spaces of parabolic symplectic orthogonal bundles on curves

TL;DR

This paper proves that moduli spaces of parabolic symplectic and orthogonal bundles on smooth curves have globally F regular type, leading to vanishing higher cohomology of theta line bundles, and introduces new methods for codimension estimation.

Contribution

It establishes the globally F regular type property for these moduli spaces and develops a novel approach to codimension estimation involving infinite Grassmannians.

Findings

Moduli spaces are globally F regular type.

Higher cohomology of theta line bundles vanishes.

Develops a new method for codimension estimation.

Abstract

We prove that the moduli spaces of parabolic symplectic/orthogonal bundles on a smooth curve are globally F regular type. As a consequence, all higher cohomology of theta line bundle vanish. During the proof, we develop a method to estimate codimension, and consider the infinite grassmannians for parabolic $G$ bundles.