Higher rank K-theoretic Donaldson-Thomas Theory of points

Abstract: A classical way to produce invariants is through intersection theory, usually on a smooth projective variety. We give a gentle introduction on how to use torus actions to refine invariants in several directions, for example K-theoretic and virtual invariants. As a concrete example, we explain how to extract meaningful invariants from the Quot schemes of quasi-projective smooth toric threefolds and how to refine them. We present and prove various closed formulas for different flavours of higher rank Donaldson-Thomas invariants of points, solving a series of conjectures proposed in String Theory. This is based on joint work with N. Fasola and A. Ricolfi.

algebraic geometrynumber theory

Audience: researchers in the topic

Leiden Algebra, Geometry, and Number Theory Seminar