Symplectic forms in algebraic geometry

Symplectic forms in algebraic geometry

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Giulia Saccà, IAS
IAS Room S-101

Imposing the existence of a holomorphic symplectic form on a projective algebraic variety is a very strong condition. After describing various instances of this phenomenon (among which is the fact that so few examples are known!), I will focus on the specific topic of maps from projective varieties admitting a holomorphic symplectic form. Essentially, the only such maps are Lagrangian fibrations and birational contractions. I will motivate why one should care about these types of maps, and give many examples illustrating their rich geometry. I will not assume background material, beyond a basic course in algebraic geometry.