Algebra and Algebraic Geometry Seminar Spring 2020

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Spring 2020 Schedule

date speaker title host(s)
January 24 Xi Chen (Alberta) Rational Curves on K3 Surfaces Michael K
January 31 Janina Letz (Utah) TBD Daniel and Michael B
February 7 Jonathan Montaño (New Mexico State) TBD Daniel
February 14
February 21 Erika Ordog (Duke) TBD Daniel
February 28
March 6
March 13
March 20
March 27 Patrick McFaddin (Fordham) TBD Michael B
April 3
April 10 Ruijie Yang (Stony Brook) TBD Michael K
April 17
April 24
May 1 Lazarsfeld Distinguished Lectures
May 8


Abstracts

Xi Chen

Rational Curves on K3 Surfaces

It is conjectured that there are infinitely many rational

curves on every projective K3 surface. A large part of this conjecture was proved by Jun Li and Christian Liedtke, based on the characteristic p reduction method proposed by Bogomolov-Hassett-Tschinkel. They proved that there are infinitely many rational curves on every projective K3 surface of odd Picard rank. Over complex numbers, there are a few remaining cases: K3 surfaces of Picard rank two excluding elliptic K3's and K3's with infinite automorphism groups and K3 surfaces with two particular Picard lattices of rank four. We have settled these leftover cases and also generalized the conjecture to the existence of curves of high genus. This is a joint work with Frank Gounelas and Christian Liedtke.