Yifeng Huang: Motivic aspects of zero-dimensional Quot schemes and Coh stacks

Yifeng Huang, USC

(Joint work with Ruofan Jiang) There are two moduli spaces of sheaves naturally associated with a variety X: the (0-dim) Quot scheme, which parametrizes 0-dim-supported quotients of a given coherent sheaf (most typically, 𝒪_X^⊕d for d ≥ 1), and the (0-dim) Coh stack, which parametrizes 0-dim-supported coherent sheaves on X. These moduli spaces widely show up in geometric representation theory, quiver varieties, Springer fibers, etc. We study their motives in the Grothendieck ring of varieties (or stacks), which is a common refinement of Euler characteristic and point count over finite fields. I will explain some general results we obtain, drawing techniques from classical algebra, hypergeometric functions, and p-adic integrals.