Picard-Fuchs equations of families of QM abelian surfaces

Amnon Besser; Ron Livné

doi:10.4310/CNTP.2018.v12.n4.a5

Picard-Fuchs equations of families of QM abelian surfaces

Amnon Besser
, Ron Livné

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We describe an algorithm for computing the Picard-Fuchs equation for a family of twists of a fixed elliptic surface. We then apply this algorithm to obtain the equations for several examples, which come from families of Kummer surfaces over Shimura curves, as studied in our previous work. We use this to find correspondences between the parameter spaces of our families and Shimura curves.

Original language	English
Pages (from-to)	829-856
Number of pages	28
Journal	Communications in Number Theory and Physics
Volume	12
Issue number	4
DOIs	https://doi.org/10.4310/CNTP.2018.v12.n4.a5
State	Published - 2018

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© by International Press of Boston, Inc.

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10.4310/CNTP.2018.v12.n4.a5

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abstract = "We describe an algorithm for computing the Picard-Fuchs equation for a family of twists of a fixed elliptic surface. We then apply this algorithm to obtain the equations for several examples, which come from families of Kummer surfaces over Shimura curves, as studied in our previous work. We use this to find correspondences between the parameter spaces of our families and Shimura curves.",

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N2 - We describe an algorithm for computing the Picard-Fuchs equation for a family of twists of a fixed elliptic surface. We then apply this algorithm to obtain the equations for several examples, which come from families of Kummer surfaces over Shimura curves, as studied in our previous work. We use this to find correspondences between the parameter spaces of our families and Shimura curves.

AB - We describe an algorithm for computing the Picard-Fuchs equation for a family of twists of a fixed elliptic surface. We then apply this algorithm to obtain the equations for several examples, which come from families of Kummer surfaces over Shimura curves, as studied in our previous work. We use this to find correspondences between the parameter spaces of our families and Shimura curves.

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JO - Communications in Number Theory and Physics

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Picard-Fuchs equations of families of QM abelian surfaces

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