Semistable sheaves with symmetric \(c_1\) on Del Pezzo surfaces of degree \(5\) and \(6\)
type: Item
instance of: scholarly article
title: Semistable sheaves with symmetric \(c_1\) on Del Pezzo surfaces of degree \(5\) and \(6\)
zbMATH Open document ID: 1475.14077
author: Takeshi Abe
published in: European Journal of Mathematics
publication date: 2021-07-15T00:00:00Z
review text: The author realizes for Del Pezzo surfaces of degree 5 and 6 the program begun by \textit{J. M. Drezet} and \textit{J. Le Potier} [Ann. Sci. Éc. Norm. Supér. (4) 18, 193--243 (1985; Zbl 0586.14007)], deepened by \textit{J. M. Drezet} [J. Reine Angew. Math. 380, 14--58 (1987; Zbl 0613.14013)] and extended by the author of the paper under review for \({\mathbb P}^1 \times {\mathbb P}^1\) [\textit{T. Abe}, Nagoya Math. J. 227, 86--159 (2017; Zbl 1415.14015)]. In this paper the following aims are realized: \begin{itemize} \item ``determine Chern classes of semistable sheaves with symmetric \(c_1\) on Del Pezzo surfaces of degree 5 and 6 (Theorem 4.8); \item define the height of the moduli space of semistable sheaves with symmetric \(c_1\) (Definition 4.9); \item show that the moduli space of height zero of semistable sheaves with symmetric \(c_1\) is isomorphic to a moduli space of representations of a certain quiver (Theorem 6.4)''. \end{itemize} It is interesting to note that the author explains why the case of Del Pezzo surfaces of degree 5 and 6 is a natural continuation of the cases \({\mathbb P}^2\) and \({\mathbb P}^1 \times {\mathbb P}^1\).
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14F08
zbMATH DE Number: 7371784
zbMATH Keywords: moduli of vector bundles
zbMATH Keywords: quiver representations
zbMATH Keywords: Bridgeland stability
zbMATH Keywords: Del Pezzo surfaces
reviewed by: Nicolae Manolache
MaRDI profile type: Publication
full work available at URL: s40879-020-00434-9
OpenAlex ID: W3120352708
cites work: SEMISTABLE SHEAVES WITH SYMMETRIC ON A QUADRIC SURFACE
cites work: Bridgeland-stable moduli spaces for \(K\)-trivial surfaces
cites work: The minimal model program for the Hilbert scheme of points on \(\mathbb P^2\) and Bridgeland stability
cites work: Bridgeland stability of line bundles on surfaces
cites work: The space of stability conditions on the local projective plane
cites work: Classical algebraic geometry. A modern view
cites work: Fibrés exceptionnels et variétés de modules de faisceaux semi-stables sur P2 ( C ).
cites work: Fibrés stables et fibrés exceptionnels sur $\mathbb{P}_2$
cites work: Effective divisors on the Hilbert scheme of points in the plane and interpolation for stable bundles
cites work: Three-block exceptional collections over Del Pezzo surfaces
cites work: EXCEPTIONAL SHEAVES ON DEL PEZZO SURFACES
cites work: Q3126815
cites work: Birational models of moduli spaces of coherent sheaves on the projective plane
cites work: Lectures on Bridgeland Stability
DOI: 10.1007/S40879-020-00434-9
description: scientific article; zbMATH DE number 7371784