Universal Kummer Families Over Shimura Curves

Amnon Besser; Ron Livné

doi:10.1007/978-1-4614-6403-7_7

Universal Kummer Families Over Shimura Curves

Amnon Besser, Ron Livné

Ben-Gurion University of the Negev, The Hebrew University of Jerusalem

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We give a number of examples of an isomorphism between two types of moduli problems. The first classifies elliptic surfaces over the projective line with five specified singular fibers, of which four are fixed and one gives the parameter; the second classifies K3 surfaces with a specified isogeny to an abelian surface with quaternionic multiplication.

Original language	American English
Title of host publication	Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds
Editors	Radu Laza, Matthias Schütt
Publisher	Springer New York
Pages	201-265
Number of pages	65
ISBN (Electronic)	9781461464037, 978-1-4614-6403-7
ISBN (Print)	9781461464020, 978-1-4614-6402-0, 978-1-4899-9918-4
DOIs	https://doi.org/10.1007/978-1-4614-6403-7_7
State	Published - Jun 2013

Publication series

Name	Springer, New York

Keywords

Discriminant forms
Elliptic surfaces
K3 surfaces
Shimura curves

Access to Document

10.1007/978-1-4614-6403-7_7

https://doi.org/10.1007/978-1-4614-6403-7_7

Cite this

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title = "Universal Kummer Families Over Shimura Curves",

abstract = "We give a number of examples of an isomorphism between two types of moduli problems. The first classifies elliptic surfaces over the projective line with five specified singular fibers, of which four are fixed and one gives the parameter; the second classifies K3 surfaces with a specified isogeny to an abelian surface with quaternionic multiplication.",

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AU - Livné, Ron

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AB - We give a number of examples of an isomorphism between two types of moduli problems. The first classifies elliptic surfaces over the projective line with five specified singular fibers, of which four are fixed and one gives the parameter; the second classifies K3 surfaces with a specified isogeny to an abelian surface with quaternionic multiplication.

KW - Discriminant forms

KW - Elliptic surfaces

KW - K3 surfaces

KW - Shimura curves

U2 - 10.1007/978-1-4614-6403-7_7

DO - 10.1007/978-1-4614-6403-7_7

M3 - Chapter

SN - 9781461464020

SN - 978-1-4614-6402-0

SN - 978-1-4899-9918-4

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A2 - Schütt, Matthias

PB - Springer New York

ER -

Universal Kummer Families Over Shimura Curves

Abstract

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