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On Shioda–Inose structures of one-parameter families of K3 surfaces

✍ Scribed by Ling Long

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 277 KB
Volume: 109
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2004.06.009

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✦ Synopsis

We develop an algorithm to determine a one-parameter family of elliptic curves associated to a one-parameter family of K3 surfaces with generic Picard number 19 by a Shioda-Inose structure. The family of elliptic curves is determined up to an isomorphism and an isogeny. An application to a generalized congruence number problem is also discussed.

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