Construction of non-Kähler Calabi-Yau manifolds by log deformations

Abstract: Calabi-Yau manifolds (in the strict sense) form an important class in the classification of algebraic varieties. One can also consider its generalisation by removing the projectivity assumption. Clemens and Friedman constructed infinitely many topological types of non-Kähler Calabi-Yau 3-folds whose 2nd Betti numbers are zero. In this talk, I will present examples of non-Kähler Calabi-Yau manifolds with arbitrarily large 2nd Betti numbers. The construction is by smoothing normal crossing varieties. The key tools of the construction are some isomorphisms between general rational elliptic surfaces which induce isomorphisms between Calabi-Yau manifolds of Schoen type.

Mathematics

Audience: researchers in the topic

Emmy Noether Kolloquium Mainz