Moduli spaces of real algebraic \(N=2\) supercurves
type: Item
instance of: scholarly article
title: Moduli spaces of real algebraic \(N=2\) supercurves
zbMATH Open document ID: 0895.58005
DOI: 10.1007/BF02509616
publication date: 1997-11-04T00:00:00Z
review text: In this article, the moduli space of real \(N=2\) supercurves is studied. \(N=2\) complex supercurves are obtained by factoring out a super-Fuchsian group from the \(N=2\) super-half-plane. Real supercurves are given by a complex supercurve with an antiholomorphic involution. The real points of the curve are the fixed points of the involution. A complete set of topological invariants of the curve is given by the genus, the number of ovals, and by connectedness (resp. non-connectedness) of the complex curve with the real points removed. The connected components of the moduli space are explicitly described and a complete set of topological invariants for the components are given. Each of the components is represented as \(\mathbb R^{(m| n)}/\text{Mod}\) of a linear superspace by a discrete group \(\text{Mod}\). The dimensions \(m\) and \(n\) are given. Depending on whether the two Arf functions coincide or not, one obtains \((m| n)=(4g-3| 4g-4)\), resp. \((4g-4| 4g-4)\). Real \(N=2\) supercurves can be mapped to real spinor bundles of rank 2 over real algebraic curves. Hence a description of the moduli space of spinor bundles of rank 2 over a real curve is obtained.
Mathematics Subject Classification ID: 58A50
Mathematics Subject Classification ID: 32C11
Mathematics Subject Classification ID: 14M30
Mathematics Subject Classification ID: 14H15
zbMATH DE Number: 1053618
zbMATH Keywords: supercurve
zbMATH Keywords: Arf function
zbMATH Keywords: super-Fuchsian group
zbMATH Keywords: moduli space of rank 2 spinor bundles
author: Sergey Natanzon
reviewed by: M. Schlichenmaier
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1053618