Major Oral: "Constructions of Calabi-Yau Manifolds from Reflexive Polytopes"

Tokio Sasaki, Washington University in Saint Louis

Abstract: One of standard constructions of a mirror pair of Calabi-Yau manifolds is given by Batyrev, as anticanonical hypersurfaces of Toric varieties associated to a reflexive polytope and its polar dual. Batyrev and Borisov also proposed the similar mirror symmetry for dual nef-partitions of reflexive polytopes. It implies the importance of the Tyurin degeneration, which is a degeneration of a Calabi-Yau manifold to two quasi-Fano varieties intersecting in a one less dimensional Calabi-Yau. This talk focuses on introducing these constructions of Calabi-Yau manifolds from reflexive polytopes and a motivated example with indecomposable higher cycles.

Host: Matt Kerr