Kummer surfaces associated with Seiberg-Witten curves
type: Item
instance of: scholarly article
title: Kummer surfaces associated with Seiberg-Witten curves
zbMATH Open document ID: 1236.14044
author: Andreas Malmendier
published in: Journal of Geometry and Physics
publication date: 2011-12-21T00:00:00Z
full work available at URL: https://arxiv.org/abs/0912.4774
review text: The author gives an explicit construction of a family of Jacobian elliptic \(K3\) surfaces with high Picard rank. More explicitly, by applying a rational transformation to the base curve \(\mathbb{CP}^{1}\) of the Seiberg-Witten curve for \(\mathcal{N}=2\) supersymmetric pure \(SU(2)\)-gauge theory, the author obtains a family of Jacobian elliptic \(K3\) surfaces of Picard rank 17. In this work, it is also shown that the desingularization of the quotient of \(K3\) surface by an involution is isomorphic to a Kummer surface of the Jacobian variety of a curve of genus two.
reviewed by: Vehbi Emrah Paksoy
Mathematics Subject Classification ID: 14J80
Mathematics Subject Classification ID: 14J27
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 81T30
zbMATH DE Number: 5991237
zbMATH Keywords: \(K3\) surfaces
zbMATH Keywords: Kummer surfaces
zbMATH Keywords: elliptic surfaces
zbMATH Keywords: Seiberg-Witten curves
MaRDI profile type: Publication
OpenAlex ID: W2038436225
arXiv ID: 0912.4774
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DOI: 10.1016/J.GEOMPHYS.2011.09.010
description: scientific article