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Collectanea Mathematica

, Volume 70, Issue 2, pp 295–321 | Cite as

Moduli spaces of bundles and Hilbert schemes of scrolls over \(\nu \)-gonal curves

  • Youngook Choi
  • Flaminio FlaminiEmail author
  • Seonja Kim
Article
  • 35 Downloads

Abstract

The aim of this paper is twofold. We first strongly improve our previous main result Choi et al. (Proc Am Math Soc 146(8):3233–3248, 2018, Theorem 3.1), concerning classification of irreducible components of the Brill–Noether locus parametrizing rank 2 semistable vector bundles of suitable degrees d, with at least \(d-2g+4\) independent global sections, on a general \(\nu \)-gonal curve C of genus g. We then uses this classification to study several properties of the Hilbert scheme of suitable surface scrolls in projective space, which turn out to be special and stable.

Keywords

Stable rank 2 bundles Brill–Noether loci General \(\nu \)-gonal curves Hilbert schemes 

Mathematics Subject Classification

14H60 14D20 14J26 

Notes

Acknowledgements

The authors thank KIAS and Dipartimento di Matematica Universita’ di Roma “Tor Vergata” for the warm atmosphere and hospitality during the collaboration and the preparation of this article. The authors are indebted to the referee for the careful reading of the first version of the paper and for valuable comments and suggestions which have certainly improved the readability of the paper.

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Copyright information

© Universitat de Barcelona 2018

Authors and Affiliations

  1. 1.Department of Mathematics EducationYeungnam UniversityGyeongsanRepublic of Korea
  2. 2.Dipartimento di MatematicaUniversita’ degli Studi di Roma Tor VergataRomeItaly
  3. 3.Department of Electronic EngineeringChungwoon UniversityIncheonRepublic of Korea

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