Maximal configurations of rational curves on K3-surfaces of high degrees

Abstract: One of unexpected consequences of the orbibundle Miyaoka-Yau-Sakai inequality is a bound on the maximal number of rational degree-d curves on smooth complex K3-surfaces of given degree obtained by Miyaoka in 2009. After recalling the necessary notions, in my talk I will present various results concerning the question whether the above bound is sharp for rational (resp. smooth rational) curves on K3-surfaces of high degree.

Based on joint work with M. Schuett (Hannover) and A. Degtyarev (Ankara).

algebraic geometry

Audience: researchers in the discipline

ODTU-Bilkent Algebraic Geometry Seminars