Seminar: (Rational) Curves on (K3) surfaces 2011/12, Tuesday 24 pm, starting October 11

The aim is to understand what is known about rational
curves on K3 surfaces.
At the same time, this will
give us the chance to learn basic techniques
in deformation theory for (stable) curves, etc.
A thorough
knowledge of algebraic geometry is necessary, some familiarity
with K3 surfaces and the language of (various) moduli
spaces helpful.
~
Preliminary program (likely to change):
Tue, 11.10.: General introduction (D. Huybrechts)
Tue, 25.10.: Existence of nodal rational curves a la Bogomolov, Mumford (St. Anschlag)
Tue, 8.11.: Deformation theory of stable maps I (M. Kemeny)
Tue, 15.11.: Deformation theory of stable maps II (M. Kemeny)
Tue, 22.11.: Existence of infinitely many rational curves on K3 with odd Picard number (after Li/Liedtke) (D. Huybrechts)
Tue, 29.11.: Endomorphisms of K3 (after Dedieu,..) (Z. Zhang, M. Lahoz)
Tue, 6.12.: T. Dedieu (Toulouse): Nonexistence of endomorphisms of generic K3 surfaces (after Chen). 2 Talks
Tue, 13.12.: Endomorphisms of K3. Part II (M. Lahoz)
Tue, 17.1.: Existence of rational curves (after Chen) (M. Kemeny)
Tue, 24.1.: Density results (after Chen, Lewis, McLean) (D. Huybrechts)Existence of rational curves (after Chen) (M. Kemeny)
B. Hassett: Rational curves on K3 surface. Lecture Notes. see his webpage F. Bogomolov, B. Hassett, Y. Tschinkel: Constructing rational curves on K3 surfaces. Duke and arxiv Xi Chen: A simple proof that rational curves on K3 are nodal. Math. Ann. S. Mori, S. Mukai: The uniruledness of the moduli space of curves of genus 11. LN 1016 W. Barth, K. Hulek, Ch. Peters, A. van de Ven: Compact complex surfaces (New edition. Special results for K3) T. Dedieu: Severi varieties and slef rational maps of K3 surfaces J. Li, Ch. Liedtke: Rational curves on K3 surfaces Xi Chen: Self rational maps of K3 surfaces Xi Chen, J. Lewis: Density of rational curves on K3 surfaces ~ For further information contact huybrech@.....