Rational curves on K3 surfaces

Abstract: We prove that every complex projective K3 surface contains infinitely rational curves, which confirms a folklore conjecture on K3 surfaces. This was previously known for elliptic K3 surfaces (Bogomolov-Tschinkel), for very general K3 surfaces (Chen), as well as for K3 surfaces of odd Picard rank (Bogomolov-Hassett-Tschinkel, Li-Liedtke). We finish this conjecture by introducing two new techniques: “regeneration” (a sort of converse to degeneration) and the “marked point trick” (a technique for controlled degenerations), which allows to treat the missing cases. This is joint work with Xi Chen and Frank Gounelas.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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