Hirschowitz, André; Laszlo, Yves Remark on the existence of stable fibre bundles on surfaces. (À propos de l’existence de fibrés stables sur les surfaces.) (French) Zbl 0848.14008 J. Reine Angew. Math. 460, 55-68 (1995). Let \(X\) be an arbitrary smooth projective surface over the complex numbers \(\mathbb{C}\). The authors show how to construct a stable vector bundle with arbitrary rank \(r\), arbitrary first Chern class \(c_1\) (viewed as an element of the Néron-Severi group \(NS (X))\), and sufficiently large second Chern class \(l\). Their proof is algebraic, showing that a generic deformation of a sufficiently singular “elementary diminution” of a fixed vector bundle \({\mathcal E}\) (with first Chern class \(c_1)\) is stable (and locally free if \(l\) is sufficiently large). This paper extends previous work by Y. Laszlo on sheaves on \(\mathbb{P}^2\) [Math. Ann. 299, No. 4, 597-608 (1994; Zbl 0846.14011)].Several other authors have obtained similar results, including D. Gieseker and J. Li, Z. Qin and W. P. Li, and M. Maruyama. Reviewer: L.G.Roberts (Kingston/Ontario) Cited in 1 Document MSC: 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 57R20 Characteristic classes and numbers in differential topology Keywords:construction of stable vector bundle Citations:Zbl 0846.14011 PDFBibTeX XMLCite \textit{A. Hirschowitz} and \textit{Y. Laszlo}, J. Reine Angew. Math. 460, 55--68 (1995; Zbl 0848.14008) Full Text: arXiv Crelle EuDML