WEEKLY ACTIVITIES

Counting surfaces on Calabi-Yau 4-folds
Speaker: Hyeonjun Park (Korea Institute For Advanced Study)

Time: 3h15 pm in Vietnam, 23/12/2022

Zoom link:

https://us02web.zoom.us/j/85114528712?pwd=Z0tyalN1MVQ0MGxKc3M0bG9sUFBxZz09

Meeting ID: 851 1452 8712

Passcode: 608225

Abstract: In this talk, we discuss counting surfaces on Calabi-Yau 4-folds. Besides the Hilbert scheme of 2-dimensional subschemes, we introduce two types of moduli spaces of stable pairs. We show that all three moduli spaces are related by GIT wall-crossing and parametrize polynomial Bridgeland stable objects in the bounded derived category. We construct reduced Oh-Thomas virtual cycles on the moduli spaces via Kiem-Li cosection localization and prove that they are deformation invariant along Hodge loci. We show that the cosections can be enhanced to (-1)-shifted closed 1-forms by generalizing the integration map of Pantev-Toen-Vaquie-Vezzosi which yields reduced (-2)-shifted symplectic derived enhancements on the moduli spaces. As an application, we show that the variational Hodge conjecture holds for any family of Calabi-Yau 4-folds supporting a non-zero reduced virtual cycle. This is joint work with Younghan Bae and Martijn Kool.

Website of the AGEA seminar:

https://sites.google.com/ncts.ntu.edu.tw/agea-seminar

Mirror site

http://www.math.ntu.edu.tw/~jkchen/agea-seminar.html

 

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