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On Shioda-Inose structures of one-parameter families of K3 surfaces |
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| Authors: | Ling Long |
| Institution: | a School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA b Department of Mathematics, Iowa State University, Ames, IA 50011, USA |
| Abstract: | 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. |
| Keywords: | Elliptic curve Isogeny Complex multiplication K3 surface Shioda-Inose structure Picard-Fuchs equation Monodromy representation |
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