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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

Manabu Ide
Manabu Ide*
Affiliation:
Graduate School of Mathematics, Nagoya University, Furō-chō, Chikusa-ku, Nagoya 464-8602, Japan
*
Tokoha Gakuen University, 1-22-1, Sena, Aoi-ku, Shizuoka-shi, 420-0911, Japan, [email protected]
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Abstract

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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.

Keywords

14H4514C2014J28
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 190 , 2008 , pp. 183 - 197
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

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