Trieste Algebraic Geometry Summer School (TAGSS) 2021 - Hyperkähler and Prym varieties: classical and new results | (smr 3609)
Starts 19 Jul 2021
Ends 23 Jul 2021
Central European Time
An ICTP Virtual Meeting
Hyperkähler manifolds are a class of manifolds with vanishing first Chern class, constituting an active area of current research. Another fundamental problem concerns moduli space of polarized abelian varieties, studied via Prym varieties and the Prym map to the moduli of abelian varieties.
Hyperkähler manifolds, an overview and some open problems
Hyperkähler manifolds 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.
The course 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, interesting connections between hyperkähler manifolds, Fano manifolds and abelian varieties will be shown.
The 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. The moduli aspect and the appearances of Prym varieties in other mathematical contexts will also be discussed.
Characterization of hyperkähler manifolds via their cohomology
Period maps from the moduli spaces of hyperkähler manifolds to the period domains of their second cohomology
Connections between hyperkähler manifolds, Fano manifolds and abelian varieties
Abelian varieties and Polarized abelian varieties
Prym varieties and the Prym map: classical theory and applications
E. IZADI, University of California, San Diego, USA
A. ORTEGA, Humboldt-Universität zu Berlin, Germany
Contributed talks: Participants interested in giving a short communication are invited to submit an abstract.