Rational curves on fibered Calabi-Yau manifolds

Luogo:  Aula Seminari “-1” – Dipartimento di Matematica
Ore 14:00

• Relatore: Diletta Martinelli (University of Edinburgh)

​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.

This scientific activity is held in the framework of the project FIRB 2012 "Moduli spaces and applications".

Referente: Claudio Fontanari