EVENT DETAILS AND ABSTRACT

Title: Rational curves on fibered Calabi-Yau manifolds
Speaker: Diletta Martinelli
Speaker Info: Univ. of Edinburgh
Brief Description:
Special Note:
Abstract:

Calabi-Yau manifolds are of interest in both algebraic geometry and theoretical physics. In particular the problem of determining whether Calabi-Yau manifolds do contain rational curves has big relevance in string theory. Moreover, a folklore conjecture in algebraic geometry predicts the existence of rational curves on every Calabi-Yau manifolds. There are several positive answers in dimension three but very little is known in higher dimension. I will talk about a joint work with Simone Diverio and Claudio Fontanari where we prove the existence of rational curves on Calabi-Yau manifolds of any dimension that admit an elliptic fibration. If time permits, I will show how to use this result to produce rational curves on Calabi-Yau manifolds that admit a fibration onto a curve whose fibers are abelian varieties.