Younghan Bae: Surfaces on Calabi–Yau 4-folds

Abstract

Let X be a smooth projective 4-fold over complex numbers with trivial canonical divisor. One can ask whether it is possible to count surfaces on X with given rational (2,2)-class. Recently Boris–Joyce/Oh–Thomas constructed a virtual cycle on the moduli space of (semi)-stable sheaves on X. On the other hand this construction often gives a trivial answer when the rational (2,2)-class has interesting Hodge theoretic information. I will explain how to fix this issue and relation to Hodge theory of (2,2) classes on Calabi-Yau 4-folds. This is a joint project with Martijn Kool and Hyeonjun Park.