K-theorietic sheaf-counting invariants of Quot^n(C^4)

Abstract: Consider the Quot scheme parametrising length n quotients of the rank r trivial bundle on C^4. There's a natural torus action on this scheme, for which the fix points are labelled by r-tuples of solid partitions of total size n. Nekrasov and Piazzalunga have assigned rational function weights to these fix points and conjectured a formula for the generating function of weighted counts of fix points. Oh and Thomas have defined general K-theoretic sheaf counting invariants for Calabi-Yau 4-folds and proved a torus localisation formula for these. We show that Nekrasov-Piazzalunga's weights agree with weights coming from the Oh-Thomas localisation formula (matching up the signs is the tricky part). We use this to prove that Nekrasov-Piazzalunga's conjectured formula for the generating function is correct. This is joint work with Martijn Kool.

algebraic geometry

Audience: researchers in the topic

Derived seminar

Series comments: https://ed-ac-uk.zoom.us/j/89993982042

Password: a simply-connected two-dimensional variety with trivial canonical bundle (omit the space)