Constructing rational curves on K3 surfaces
Bogomolov, Fedor ; Hassett, Brendan ; Tschinkel, Yuri
Duke Math. J., Tome 156 (2011) no. 1, p. 535-550 / Harvested from Project Euclid
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We develop a mixed-characteristic version of the Mori-Mukai technique for producing rational curves on K $3$ surfaces. We reduce modulo $p$ , produce rational curves on the resulting K $3$ surface over a finite field, and lift to characteristic zero. As an application, we prove that all complex K $3$ surfaces with Picard group generated by a class of degree two have an infinite number of rational curves.
Publié le : 2011-04-15
Classification:  14J28,  14D15,  14D10 
@article{1301678732,
     author = {Bogomolov, Fedor and Hassett, Brendan and Tschinkel, Yuri},
     title = {Constructing rational curves on K3 surfaces},
     journal = {Duke Math. J.},
     volume = {156},
     number = {1},
     year = {2011},
     pages = { 535-550},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1301678732}
}

Bogomolov, Fedor; Hassett, Brendan; Tschinkel, Yuri. Constructing rational curves on K3 surfaces. Duke Math. J., Tome 156 (2011) no. 1, pp.  535-550. http://gdmltest.u-ga.fr/item/1301678732/