The determinant line bundle over moduli spaces of instantons on abelian surfaces
type: Item
instance of: scholarly article
title: The determinant line bundle over moduli spaces of instantons on abelian surfaces
zbMATH Open document ID: 0806.14035
DOI: 10.1007/BF02571947
author: Antony Maciocia
published in: Mathematische Zeitschrift
publication date: 1994-12-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174693
review text: We study the determinant line bundle over the moduli space of stable bundles on abelian surfaces. We evaluate their analytic torsions. We extend Mukai's version of the Parseval theorem to \(L^ 2\) metrics on cohomology groups. We prove that the Mukai transform preserves the determinant line bundle as a hermitian line bundle. This is done by induction via the natural boundary of the moduli spaces.
Mathematics Subject Classification ID: 14M12
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14K99
zbMATH DE Number: 704951
zbMATH Keywords: instantons
zbMATH Keywords: determinant line bundle over moduli space of stable bundles
zbMATH Keywords: abelian surfaces
zbMATH Keywords: torsion
zbMATH Keywords: Mukai transform
MaRDI profile type: Publication
cites work: Q5749404
cites work: The analysis of elliptic families. I: Metrics and connections on determinant bundles
cites work: Analytic torsion and holomorphic determinant bundles. I: Bott-Chern forms and analytic torsion. II: Direct images and Bott-Chern forms. III: Quillen metrics on holomorphic determinants
cites work: Q3972472
cites work: Nahm's transformation for instantons
cites work: Instanton moduli as a novel map from tori to K3-surfaces
cites work: Infinite determinants, stable bundles and curvature
cites work: The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
cites work: Resolution of singularities of an algebraic variety over a field of characteristic zero. I
cites work: Algebraic geometric interpretation of Donaldson's polynomial invariants
cites work: Semi-homogeneous vector bundles on an abelian variety
cites work: Duality between D(X) and with its application to picard sheaves
cites work: Symplectic structure of the moduli space of sheaves on an abelian or K 3 surface
cites work: Determinants of Cauchy-Riemann operators on a Riemann surface
cites work: Analytic torsion for complex manifolds
description: scientific article; zbMATH DE number 704951