Constructing rational curves on K3 surfaces

Research output: Contribution to journalArticle

Abstract

We develop a mixed-characteristic version of the Mori-Mukai technique for producing rational curves on K3 surfaces. We reduce modulo p, produce rational curves on the resulting K3 surface over a finite field, and lift to characteristic zero. As an application, we prove that all complex K3 surfaces with Picard group generated by a class of degree two have an infinite number of rationalcurves.

Original languageEnglish (US)
Pages (from-to)535-550
Number of pages16
JournalDuke Mathematical Journal
Volume157
Issue number3
DOIs
StatePublished - Apr 15 2011

Fingerprint

K3 Surfaces
Rational Curves
Picard Group
Galois field
Modulo
Zero

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Constructing rational curves on K3 surfaces. / Bogomolov, Fedor; Hassett, Brendan; Tschinkel, Yuri.

In: Duke Mathematical Journal, Vol. 157, No. 3, 15.04.2011, p. 535-550.

Research output: Contribution to journalArticle

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