Erratum: ``Projective moduli for Hitchin pairs''.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1055.14503
DOI: 10.1142/S0129167X00000295
author: Alexander Schmitt
published in: International Journal of Mathematics
publication date: 2001-08-01T00:00:00Z
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14H60
zbMATH DE Number: 1629358
MaRDI profile type: Publication
title: Erratum: ``Projective moduli for Hitchin pairs''.
review text: Concerns the author's paper in Int. J. Math. 9, No. 1, 107--118 (1998; Zbl 0936.14009).NEWLINEFrom the text: ''The construction of the moduli space of Hitchin pairs in my paper contains a removable error. Namely, the parameter space \(\mathfrak P\) constructed in Section 4 is not the good one.NEWLINEThe correct parameter space \(\mathfrak R\) is constructed in the obvious way as a closed subscheme of the following projective bundle \(\widetilde{\mathfrak R}\) over the quot scheme \(\mathfrak Q\): NEWLINE\[NEWLINE\widetilde{\mathfrak R}:={\mathbb P}({\mathcal O}_{\mathfrak Q}\oplus\pi_{{\mathfrak Q}*}({\mathfrak E}_{\mathfrak Q}\otimes\pi^*_X{\mathcal O}_X(\nu+m))^\vee\otimes\pi_{{\mathfrak Q}*}({\mathfrak E}_{\mathfrak Q}\otimes\pi^*_X{\mathcal O}_X(\nu))).NEWLINE\]NEWLINE One checks easily that, for the space \(\mathfrak R\), the statement corresponding to Proposition 5.1 is correct.
description: scientific article; zbMATH DE number 1629358