Compactifications of the period space of Enriques surfaces. I
type: Item
instance of: scholarly article
title: Compactifications of the period space of Enriques surfaces. I
zbMATH Open document ID: 0736.14017
DOI: 10.1007/BF02571372
author: Hans Sterk
published in: Mathematische Zeitschrift
publication date: 1992-06-25T00:00:00Z
full work available at URL: https://eudml.org/doc/174253
review text: Projective degenerations of Enriques surfaces (i.e. regular compact complex surfaces with canonical class \(K_ X\) such that \(K_ X\not\sim0\), \(2K_ X\sim0\)) were classified by \textit{J. Shah} [Math. Ann. 256, 475-495 (1981; Zbl 0445.14015)]. The author studies degenerations of Enriques surfaces from the point of view of the period space. The period space considered in the paper is actually a covering of the one studied by Horikawa and Namikawa. In part I of the paper the author considers the Satake-Baily-Borel compactification of the period space and determines its boundary components using results of Looijenga and Vinberg. He proceeds with establishing a relation between his list of boundary components and Shah's list of degenerations. --- In the second part of the paper the author constructs another compactification of the period space (actually a blow up of the Satake-Baily-Borel one) which is more suitable for interpreting Shah's results.
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 32G20
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 32J25
zbMATH DE Number: 10465
zbMATH Keywords: period map
zbMATH Keywords: degeneration of Enriques surfaces
zbMATH Keywords: Satake-Baily-Borel compactification of the period space
reviewed by: F. L. Zak
MaRDI profile type: Publication
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OpenAlex ID: W2027981083
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description: scientific article; zbMATH DE number 10465