The Michigan Mathematical Journal

Connected Components of the Moduli of Elliptic $K3$ Surfaces

Abstract

The combinatorial type of an elliptic $K3$ surface with a zero section is the pair of the $\mathit{ADE}$-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
Revised: 19 August 2017
First available in Project Euclid: 14 June 2018

https://projecteuclid.org/euclid.mmj/1528941621

Digital Object Identifier
doi:10.1307/mmj/1528941621

Mathematical Reviews number (MathSciNet)
MR3835563

Zentralblatt MATH identifier
06969983

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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