Finite generation of the algebra of type A conformal blocks via birational geometry II: higher genus

Abstract

We prove finite generation of the algebra of type A conformal blocks over arbitrary stable curves of any genus. As an application we construct a flat family of irreducible normal projective varieties over the moduli stack of stable pointed curves, whose fiber over a smooth curve is a moduli space of semistable parabolic bundles. This generalizes a construction of a degeneration of the moduli space of vector bundles presented in a recent work of Belkale and Gibney.

27 pages, Revised, Published version in Proceedings of the London Mathematical Society (2020)

References in corpus (3)

• The moduli stack of $G$-bundles
• The algebra of $S{L}_3(\mathbb{C})$ conformal blocks
• Stability of vector bundles on curves and degenerations

Cited by in corpus (1)

• Positivity of the Poincaré bundle on the moduli space of vector bundles and its applications