Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T00:30:59.591Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of Vector Bundles on Curves and Degenerations

Published online by Cambridge University Press:  20 November 2018

Brian Osserman
Brian Osserman*
Affiliation:
Department of Mathematics, University of California, Davis, Davis, California, USA e-mail: osserman@math.ucdavis.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We introduce a weaker notion of (semi)stability for vector bundles on reducible curves that does not depend on a choice of polarization and suffices for many applications of degeneration techniques. We explore the basic properties of this alternate notion of (semi)stability. In a complementary direction, we record a proof of the existence of semistable extensions of vector bundles in suitable degenerations.

Keywords

14D0614H60vector bundlestabilitydegeneration
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 4 , 01 December 2016 , pp. 858 - 864
Copyright
Copyright © Canadian Mathematical Society 2016

References

[HL97] Huybrechts, D. and Lehn, M., The geometry of moduli spaces of sheaves. Aspects of Mathematics, E31, Friedr. Vieweg & Sohn, Braunschwieg, 1997.Google Scholar
[OT] Osserman, B. and Teixidor i Bigas, M., Linked symplectic forms and limit linear series in rank 2 with special determinant. Adv. Math. 288(2016), 576–630. http://dx.doi.Org/10.1016/j.aim.2015.09.030 Google Scholar
[Tei95] Teixidor i Bigas, M., Moduli spaces of vector bundles on reducible curves. Amer. J. Math. 117(1995), no. 1, 125–139. http://dx.doi.Org/10.2307/2375038 Google Scholar
[TeiO4] Teixidor i Bigas, M., Rank two vector bundles with canonical determinant. Math. Nachr. 265(2004), 100–106. http://dx.doi.Org/10.1OO2/mana.2OO310138 Google Scholar
[TeiO8] Teixidor i Bigas, M., Petri map for rank two bundles with canonical determinant. Compos. Math. 144(2008), no. 3, 705–720. http://dx.doi.Org/10.1112/S0010437X07003442 Google Scholar
[Zha] Zhang, N., Towards the Bertram-Feinberg-Mukai conjecture. To appear, J. Pure and Appl. Algebra, http://dx.doi.Org/!0.1016/j.jpaa.2O15.09.020 Google Scholar