Coursera Spring Sale
40% Off Coursera Plus Annual!
Grab it
Explore advanced topics in algebraic geometry through this comprehensive summer school covering hyperkähler manifolds and Prym varieties. Delve into hyperkähler manifolds, a class of manifolds with vanishing first Chern class that represent an active area of current research, characterized primarily by their second cohomology and featuring rare surjective period maps from moduli spaces to period domains. Study the fundamental problem of moduli spaces of polarized abelian varieties through Prym varieties and the Prym map, examining classical theory and recent advances with special focus on low genera cases that display beautiful geometric properties. Learn about generalities of abelian varieties, the Hitchin fibration, tropical Prym varieties, involutions of cubic fourfolds, and degree computations for Prym maps of étale double coverings and triple cyclic coverings. Discover interesting connections between hyperkähler manifolds, Fano manifolds, and abelian varieties while exploring moduli aspects and appearances of Prym varieties in various mathematical contexts. Participate in exercise sessions and examine topics including ramified Prym maps, geometry of Prym semicanonical pencils, Kirchhoff's theorem, and finite Prym maps through detailed lectures and problem-solving sessions.
