Algebraic Geometry SeminarㅣSurfaces on Calabi-Yau 4-folds.

Abstract: We will discuss enumerative aspects of moduli spaces of sheaves on Calabi-Yau 4-folds. In the first introductory part, I will review virtual cycles on moduli spaces of Calabi-Yau 4-folds constructed by Borisov-Joyce/Oh-Thomas. The constructions both reply on the additional properties of the moduli spaces of sheaves on Calabi-Yau 4-folds. I will also explain situations where BJ/OT classes can be related to other curve counting theories such as Gromov-Witten theory of Calabi-Yau 4-folds or Fano/Calabi-Yau 3-folds. In the second part, I will explain a theory counting surfaces on Calabi-Yau 4-folds and connection to Hodge theory. The BJ/OT class often vanishes when the surface classes are nontrivial. We will fix this issue and construct a reduced virtual cycle which contains nontrivial information. This class is deformation invariant along the Hodge locus of the surface class. This part is a joint work with Martijn Kool and Hyeonjun Park. 

 

Organizers : Sungmun Cho, Kyoung-Seog Lee, Jihun Park

 

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