Stable vector bundles with \(\chi=0\) on a simple abelian surface
type: Item
instance of: scholarly article
title: Stable vector bundles with \(\chi=0\) on a simple abelian surface
zbMATH Open document ID: 0958.14035
author: Cristian Anghel
published in: Mathematische Annalen
publication date: 2001-04-03T00:00:00Z
review text: The author produces a birational description of one component of \({\mathcal M}_X(2,D,0)\), the moduli space of stable rank \(2\) bundles with ample determinant \(D\) and Euler characteristic \(0\) over a simple abelian surface \(X\). Indeed if \(g=1+D^2/2\) and \(\phi_D:X\to \widehat X\) is the isogeny associated to \(D\), then he defines the divisor \(\widetilde D\) on \(\widehat X\) by the relation \(d\widetilde D=(\phi_D)_*D\). The author uses the Fourier transform from \(X\) to \(\widehat X\) to prove that \({\mathcal M}_X(2,D,0)\) has one component birational to the relative Jacobian \({\mathcal J}^{g-3}\) over \(\{ \widetilde D\}\), the space of curves algebraically equivalent to \(\widetilde D\).
reviewed by: Luca Chiantini
Mathematics Subject Classification ID: 14K10
Mathematics Subject Classification ID: 14K30
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14K02
zbMATH DE Number: 1384377
zbMATH Keywords: abelian surfaces
zbMATH Keywords: moduli space of stable rank 2 bundles
zbMATH Keywords: isogeny
zbMATH Keywords: Fourier transform
zbMATH Keywords: relative Jacobian
MaRDI profile type: Publication
full work available at URL: s002080050325
OpenAlex ID: W2040871376
DOI: 10.1007/S002080050325
description: scientific article; zbMATH DE number 1384377