Quantum Lefschetz without curves
Organizers
Speaker
Richard Thomas
Time
Thursday, March 7, 2024 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
The original “Quantum Lefschetz principle” enumerated genus 0 curves in a quintic 3-fold by considering them as curves in ℙ^4 and then imposing the constraint that the quintic polynomial vanishes on them.
I will review how this has to be modified in higher genus using the “p-fields” of Chang-Li and Guffin-Sharpe-Witten. Then I will describe joint work with Jeongseok Oh developing a general theory, independent of curve counting. The upshot is two formulae for the virtual cycle of a quasi-smooth derived scheme (or DM stack) cut out of another quasi-smooth derived scheme by a section of a 2-term complex of vector bundles.