University of Cambridge > Talks.cam > Algebraic Geometry Seminar > Irreducible rational curves in a K3 surface

Irreducible rational curves in a K3 surface

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  • UserJun Li (Stanford)
  • ClockWednesday 26 January 2011, 14:15-15:15
  • HouseMR13, 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 Bogomolov-Hassett-Tschinkel, which uses that all (non-supersingular) 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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