Rationality of moduli space of torsion-free sheaves over reducible curve
type: Item
instance of: scholarly article
title: Rationality of moduli space of torsion-free sheaves over reducible curve
zbMATH Open document ID: 1391.14019
author: A. Dey
author: B. N. Suhas
published in: Journal of Geometry and Physics
publication date: 2018-04-27T00:00:00Z
review text: Let \(k\) be an algebraically closed field of characteristic \(0\) and let \(C\) be a connected nodal curve over \(k\) such that each of its irreducible components has at most \(2\) nodes (the authors call such a curve a \textit{chain-like curve}). Let \(\text{M}(2,\underline{w}, \chi)\) be the moduli space of rank \(2\) torsion-free sheaves \(\underline{w}\)-semistable sheaves of Euler characteristic \(\chi\) over \(C\), where \(\chi\) is an odd integer number and \(\underline{w}\) is a polarization on \(C\) for which semi-stability and stability coincide. The main result of this paper is that the closure of the locus of stable rank \(2\) vector bundles in each irreducible component of \(\text{M}(2,\underline{w}, \chi)\) is rational. Most of the article is devoted to construct a stable family of rank \(2\) vector bundles over \(C\), paramatrized by a non-empty open subset of an affine space, which plays a fundamental role in the proof of the main theorem.
reviewed by: Michele Savarese
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14E08
zbMATH DE Number: 6865364
zbMATH Keywords: vector bundles
zbMATH Keywords: moduli space
zbMATH Keywords: rationality
zbMATH Keywords: nodal curves
MaRDI profile type: Publication
full work available at URL: j.geomphys.2018.02.009
OpenAlex ID: W2801801765
cites work: Rationality of moduli spaces of stable bundles
cites work: Correction: ''Rationally of moduli spaces of stable bundles''
cites work: Rationality of moduli of vector bundles on curves.
cites work: Rationality of Moduli Spaces of Parabolic Bundles
cites work: Rationality and Poincare Families for Vector Bundles with Extra Structure on a Curve
cites work: Some moduli stacks of symplectic bundles on a curve are rational
cites work: Rationality of the Moduli Space of Stable Pairs over a Complex Curve
cites work: Brauer Group and Birational Type of Moduli Spaces of Torsionfree Sheaves on a Nodal Curve
cites work: On a relative Mumford-Newstead theorem
cites work: On the rationality of Nagaraj-Seshadri moduli space
cites work: Q3665240
cites work: Moduli spaces of (semi)stable vector bundles on tree-like curves
cites work: Degenerations of the moduli spaces of vector bundles on curves. I
cites work: Universal families of extensions
cites work: Moduli of vector bundles on a compact Riemann surface
cites work: Basic Algebraic Geometry 1
DOI: 10.1016/J.GEOMPHYS.2018.02.009
description: scientific article; zbMATH DE number 6865364