The Michigan Mathematical Journal

Connected Components of the Moduli of Elliptic K3 Surfaces

Ichiro Shimada

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Abstract

The combinatorial type of an elliptic K3 surface with a zero section is the pair of the ADE-type of the singular fibers and the torsion part of the Mordell–Weil group. We determine the set of connected components of the moduli of elliptic K3 surfaces with fixed combinatorial type. Our method relies on the theory of Miranda and Morrison on the structure of a genus of even indefinite lattices and on computer-aided calculations of p-adic quadratic forms.

Article information

Source
Michigan Math. J., Volume 67, Issue 3 (2018), 511-559.

Dates
Received: 17 October 2016
Revised: 19 August 2017
First available in Project Euclid: 14 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1528941621

Digital Object Identifier
doi:10.1307/mmj/1528941621

Mathematical Reviews number (MathSciNet)
MR3835563

Zentralblatt MATH identifier
06969983

Subjects
Primary: 14J28: $K3$ surfaces and Enriques surfaces 11E81: Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]

Citation

Shimada, Ichiro. Connected Components of the Moduli of Elliptic $K3$ Surfaces. Michigan Math. J. 67 (2018), no. 3, 511--559. doi:10.1307/mmj/1528941621. https://projecteuclid.org/euclid.mmj/1528941621


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