TAGSS IV -
Hyperkähler and Prym varieties: classical and new results

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The school will feature courses by:

Elham Izadi -  University of California, San Diego

Hyperkähler manifolds, an overview and some open problems

Hyperkähler manifolds are a class of manifolds with vanishing first Chern class and constitute a very active area of current research. They are mainly characterized by their second cohomology. The period maps from the moduli spaces of hyperkähler manifolds to the period domains of their second cohomology are surjective, which is a rare phenomenon happening almost exclusively in weight 1 and weight 2.
We will give an introduction to hyperkähler manifolds and their known examples, survey some of the known results, and present some open problems. In the examples, we will see interesting connections between hyperkähler manifolds, Fano manifolds and abelian varieties.

and

Angela Ortega  - Humboldt Universität, Berlin

Prym varieties

A fundamental problem in algebraic geometry is to understand the moduli space of polarized abelian varieties.  This can be done via Prym varieties and its corresponding Prym map to the moduli of abelian varieties.
In this course we will review the classical theory and recent advances on Prym varieties and the Prym map,  with special focus on the low genera cases which display beautiful geometry.
We will also discuss the moduli aspect and the appearances of Prym varieties in other mathematical contexts.