TY - JOUR
T1 - Constructing rational curves on K3 surfaces
AU - Bogomolov, Fedor
AU - Hassett, Brendan
AU - Tschinkel, Yuri
PY - 2011/4/15
Y1 - 2011/4/15
N2 - 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.
AB - 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.
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U2 - 10.1215/00127094-1272930
DO - 10.1215/00127094-1272930
M3 - Article
AN - SCOPUS:79955646937
SN - 0012-7094
VL - 157
SP - 535
EP - 550
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 3
ER -