Virtual cycle on the moduli space of maps to a complete intersection

Abstract: 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.

algebraic geometry

Audience: researchers in the topic

Comments: The discussion for Rachel Webb’s talk is taking place not in zoom-chat, but at tinyurl.com/2020-09-18-rw (and will be deleted after 3-7 days).

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Stanford algebraic geometry seminar

Series comments: This seminar requires both advance registration, and a password. If you have registered once, you are always registered. Register at stanford.zoom.us/meeting/register/tJEvcOuprz8vHtbL2_TTgZzr-_UhGvnr1EGv Password: 362880

More seminar information (including slides and videos, when available): agstanford.com

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