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

[摘要] 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. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-01

[关键词] elliptic curve;isogeny;complex multiplication;K3 surface;Shioda-Inose structure;Picard-Fuchs equation;monodromy representation