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

Department 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 - 1 Jan 2018

ASJC Scopus subject areas

Algebra and Number Theory
Mathematical Physics
General Physics and Astronomy

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10.4310/CNTP.2018.v12.n4.a5

Cite this

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title = "Picard-Fuchs equations of families of QM abelian surfaces",

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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AU - Livné, Ron

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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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U2 - 10.4310/CNTP.2018.v12.n4.a5

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M3 - Article

AN - SCOPUS:85060181258

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EP - 856

JO - Communications in Number Theory and Physics

JF - Communications in Number Theory and Physics

IS - 4

ER -

Picard-Fuchs equations of families of QM abelian surfaces

Abstract

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