Stabilité du fibré tangent des surfaces de Del Pezzo. (Stability of the tangent bundle of Del Pezzo surfaces)
type: Item
instance of: scholarly article
title: Stabilité du fibré tangent des surfaces de Del Pezzo. (Stability of the tangent bundle of Del Pezzo surfaces)
zbMATH Open document ID: 0672.14009
DOI: 10.1007/BF01457509
author: Rachid Fahlaoui
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164501
review text: The author shows: For S a (complex) projective surface with ample anti- canonical bundle, the tangent bundle is semistable with respect to the polarization -K. - For \(S\neq {\mathbb{P}}^ 1\times {\mathbb{P}}^ 1,\quad {\mathbb{P}}^ 2\quad with\) a blown-up point, the tangent bundle is stable with respect to -K. Compare this result with: if \(S_ r{\mathbb{P}}^ 2\) with r blown-up points (3\(\leq r\leq 8)\) admits a Kähler-Einstein metric [conjectured] then \(S_ r\) has a semistable tangent bundle.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 4099463
zbMATH Keywords: stability of the tangent bundle of Dal Pezzo surfaces
zbMATH Keywords: Kähler-Einstein metric
MaRDI profile type: Publication
OpenAlex ID: W1968710736
description: scientific article; zbMATH DE number 4099463