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Every Curve of Genus not Greater Than Eight Lies on a K3 Surface
Published online by Cambridge University Press: 11 January 2016
Abstract
Let C be a smooth irreducible complete curve of genus g ≥ 2 over an algebraically closed field of characteristic 0. An ample K3 extension of C is a K3 surface with at worst rational double points which contains C in the smooth locus as an ample divisor.
In this paper, we prove that all smooth curve of genera. 2 ≤ g ≤ 8 have ample K3 extensions. We use Bertini type lemmas and double coverings to construct ample K3 extensions.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2008
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