Modular map for the family of abelian surfaces via elliptic K3 surfaces

Atsuhira Nagano; Hironori Shiga

doi:10.1002/mana.201300142

Modular map for the family of abelian surfaces via elliptic K3 surfaces

Atsuhira Nagano, Hironori Shiga^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

In this paper we give explicit modular maps for the family of abelian surfaces and that of the abelian surfaces whose endomorphism algebra contains Z[1+5/2]. We obtain a description of the Shimura variety for the latter family, also. The notion of the family of K3 surfaces with a fixed marking plays a central role. As the basement of our study we use the expressions of those families given by Clingher-Doran, A. Nagano and the work of A. Kumar as well.

Original language	English
Pages (from-to)	89-114
Number of pages	26
Journal	Mathematische Nachrichten
Volume	288
Issue number	1
DOIs	https://doi.org/10.1002/mana.201300142
Publication status	Published - 2015 Jan 1

Keywords

Abelian surfaces
Hilbert modular forms
K3 surfaces
Period domains
Theta constants

ASJC Scopus subject areas

Mathematics(all)

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10.1002/mana.201300142

Cite this

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AB - In this paper we give explicit modular maps for the family of abelian surfaces and that of the abelian surfaces whose endomorphism algebra contains Z[1+5/2]. We obtain a description of the Shimura variety for the latter family, also. The notion of the family of K3 surfaces with a fixed marking plays a central role. As the basement of our study we use the expressions of those families given by Clingher-Doran, A. Nagano and the work of A. Kumar as well.

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KW - Hilbert modular forms

KW - K3 surfaces

KW - Period domains

KW - Theta constants

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Modular map for the family of abelian surfaces via elliptic K3 surfaces

Abstract

Keywords

ASJC Scopus subject areas

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