Irreducible rational curves in a K3 surface
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 Jun Li (Stanford)
 Wednesday 26 January 2011, 14:1515:15
 MR13, CMS.
If you have a question about this talk, please contact Burt Totaro.
We prove that every K3 surface of odd Picard number has infinitely many
irreducible rational curves.
The proof follows the method of BogomolovHassettTschinkel, which uses that all (nonsupersingular) K3
surfaces over finite
fields have even Picard number. Using what we
call “rigidifiers” and reduction to characteristic p, we
construct rational curves of arbitrarily high degree
by deforming rigid stable maps.
This talk is part of the Algebraic Geometry Seminar series.
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