Symplectic manifolds of Fano and Calabi-Yau type

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• Dmitri Panov (Imperial College)
• Wednesday 10 March 2010, 14:30-15:30
• MR13, CMS.

If you have a question about this talk, please contact Caucher Birkar.

In this talk we discuss an attempt to understand which properties of algebraic Fano and Calabi-Yau manifolds hold for their symplectic analogues (symplectic manifolds (M,w) with c_1(M)=w, and c_1(M)=0 correspondingly). One of the goals is to construct symplectic non-algebraic examples.

Using hyperbolic geometry we show that starting from real dimension 6 the gap between algebraic and “symplectic Calabi-Yau” manifolds is huge. In the same way in each even dimension starting from 12 there exist infinite number of topological types of “symplectic Fano manifolds”. If the time permits we will discuss unirulledness. This is a joint work (in progress) with Joel Fine and Anton Petrunin.

This talk is part of the Algebraic Geometry Seminar series.

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