Counting curves in critical locus via logarithmic compactifications

Abstract: I will introduce some recent developments and work in progress on studying Gauged Linear Sigma Models using logarithmic compactifications.

These logarithmic compactifications admit two types of virtual cycles --- the reduced virtual cycles that recover Gromov-Witten invariants of complete intersections, and the canonical virtual cycles that depend only on the geometry of ambient spaces. These two types of virtual cycles differ only by a third virtual cycle of the boundary of the logarithmic compactifications. Using the punctured logarithmic maps of Abramovich-Chen-Gross-Siebert, these virtual cycles can be computed via the tropical and equivariant geometry of the logarithmic compactifications. This leads to a new method for computing Gromov-Witten invariants of complete intersections.

The talk consists of joint work with Felix Janda, Yongbin Ruan, Adrien Sauvaget and Rachel Webb.

algebraic geometry

Audience: researchers in the topic

UBC Vancouver Algebraic Geometry Seminar

Series comments: Recordings and slides are available on the seminar webpage:

wiki.math.ubc.ca/mathbook/alggeom-seminar/Main_Page