Some new results on curves on K3s - Special session of the HyperK seminar in Bonn on January 9 & 10, 2025

by Frank Gounelas (Bonn)

Thursday Jan 9, 2025, 10:30 AM → 11:30 AM Europe/Berlin

Poppelsdorfer Allee 45, 1, EG, Lecture room - HIM PA82 (HIM)

There are numerous questions and open conjectures about the (non-)existence of curves on K3 surfaces which vary maximally in moduli, or, respectively, do not vary at all (the isotrivial case) - a classical open problem in the area, which goes back to Deligne/Schoen/Serre is whether a very general K3 surface can be dominated by the product of two smooth curves. In this talk will summarise some recent results and in particular focus on recent work with Chen and Dutta proving that if the Picard rank is one, then there can be no generically smooth isotrivial families of curves.

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