Toric contact cycles in the moduli space of curves

Dhruv Ranganathan (Cambridge)

05-Aug-2021, 12:00-13:00 (3 years ago)

Abstract: The toric contact cycles are loci in the moduli space of curves that parameterize those curves that admit a morphism to a fixed toric variety, with prescribed tangency data with the toric boundary. The cycles are the fundamental building blocks in higher genus logarithmic Gromov-Witten theory and are higher dimensional analogues of the double ramification cycles, which have been studied intensely in the last decade. In recent work, Sam Molcho (ETH) and I proved that these cycles lie in the tautological part of the Chow ring of the moduli space of curves. A lesson I learned from this project, and earlier work with Navid Nabijou (Cambridge), is that it can be quite profitable to blend Fulton’s analysis of blowups and strict transforms with logarithmic Gromov-Witten theory and its virtual class. I’ll try to give a sense of the basic geometric phenomena, and point to some other places where they come up.

algebraic geometrycombinatorics

Audience: researchers in the topic


Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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