Abstract for the talk on 31.03.2020 (18:20 h)

Nonlinear Algebra Seminar Online (NASO)

Valeria Bertini (Technical University Chemnitz)
Hyperkähler manifolds and rational curves
31.03.2020, 18:20 h, MPI für Mathematik in den Naturwissenschaften Leipzig, only video broadcast

I will introduce Hyperkähler manifolds, a class of manifolds very much studied in complex algebraic geometry; they can be thought as a higher dimensional alanogue of K3 surfaces. I will present a geometrical problem on them, that is the existence of rational curves, i.e. curves birational to a projective line; the problem has a complete solution in the case of K3 surfaces, but much less is known in the Hyperkähler case.