Vector bundles on the moduli space of curves from vertex operator algebras

Abstract: Algebraic structures like vector bundles, their sections, ranks, and characteristic classes, give information about spaces on which they are defined. The stack parametrizing families of stable n-pointed curves of genus g, and the space that (coarsely) represents it, give insight into curves and their degenerations, are prototypes for moduli of higher dimensional varieties, and are interesting objects of study in their own right. Vertex operator algebras (VOAs) and their representation theory, have had a profound influence on mathematics and mathematical physics, playing a particularly important role in understanding conformal field theories, finite group theory, and invariants in topology. In this talk I will discuss vector bundles on moduli of curves defined by certain representations of VOAs.

algebraic geometry

Audience: researchers in the topic

UC Davis algebraic geometry seminar