Rational Curves on Irriducible Holomorphic Symplectic Varieties of OG10-type

July 15, 2019
Versione stampabile

Venue: Seminar Room "-1" - Department of Mathematics – Via Sommarive, 14 - Povo Trento

Hour: 2:00 p.m.

  • Valeria Bertini - PhD in Mathematics - Università degli Studi di Roma "Tor Vergata"

Thanks to some recent works due to F. Charles, G. Mongardi and G. Pacienza, we know that, in order to show the existence of rational curves on an irreducible holomorphic symplectic (IHS) variety of fixed deformation type, it is enough to do it for special points of their moduli space, thanks to the study of the monodromy group Mon^2 of the variety. 
In this talk I will start introducing the problem of finding rational curves on IHS varieties and presenting some motivation behind it; then I will describe the strategy of the authors above, focusing on a completely solved case: the Hilbert scheme of points of a general K3 surface. Finally I will present my contribution to the OG10-case, giving an example of uniruled divisor on a OG10-variety and describing the monodromy invariants of this divisor.

Contact person: Natascia Zangani