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Virtual Cycle on the Moduli Space of Maps to a Complete Intersection.

Banff International Research Station for Mathematical Innovation and Discovery

A driving question in Gromov-Witten theory is to relate the invariants of a complete intersection to the invariants of the ambient variety. In genus-zero this can often be done with a ``twisted theory,'' but this fails in higher genus. Several years ago, Chang-Li presented the moduli space of p-fields as a piece of the solution to the higher-genus problem, constructing the virtual cycle on the space of maps to the quintic 3-fold as a cosection localized virtual cycle on a larger moduli space (the space of p-fields). Their result is analogous to the classical statement that the Euler class of a vector bundle is the class of the zero locus of a generic section. I will discuss work joint with Qile Chen and Felix Janda where we extend Chang-Li's result to a more general setting, a setting that includes standard Gromov-Witten theory of smooth orbifold targets and quasimap theory of GIT targets. This work is joint with Qile Chen and Felix Janda.

Mathematics; Algebraic geometry

video/mp4

Author affiliation: University of Michigan

2020-05-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74532

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/