Tsung-Ju Lee:Mirror symmetry and Calabi--Yau fractional complete intersections

Abstract: Recently, Hosono, Lian, Takagi, and Yau studied the family of K3 surfaces arising from double covers of \(\mathbf{P}^{2}\) branch over six lines in general position and proposed a singular version of mirror symmetry. 

In this talk, I will review their results on K3 surfaces and introduce a construction of mirror pairs of certain singular Calabi--Yau varieties based on Batyrev and Borisov's dual nef-partitions. I will discuss the topological test as well as the quantum test on these singular Calabi--Yau pairs. If time permits, I will also discuss some relevant results on the B side of these singular Calabi--Yau varieties. This is based on the joint works with S. Hosono, B. Lian and S.-T. Yau.