Holomorphic triples of genus 0

Stefano Pasotti; Francesco Prantil

Open Mathematics (2008)

  • Volume: 6, Issue: 1, page 129-142
  • ISSN: 2391-5455

Abstract

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Here we study the relationship between the stability of coherent systems and the stability of holomorphic triples over a curve of arbitrary genus. Moreover we apply these results to study some properties and give some examples of holomorphic triples on the projective line.

How to cite

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Stefano Pasotti, and Francesco Prantil. "Holomorphic triples of genus 0." Open Mathematics 6.1 (2008): 129-142. <http://eudml.org/doc/269439>.

@article{StefanoPasotti2008,
abstract = {Here we study the relationship between the stability of coherent systems and the stability of holomorphic triples over a curve of arbitrary genus. Moreover we apply these results to study some properties and give some examples of holomorphic triples on the projective line.},
author = {Stefano Pasotti, Francesco Prantil},
journal = {Open Mathematics},
keywords = {Holomorphic triples; coherent systems; vector bundles; projective line; epistability; coherent system; stable vector bundle; vector bundles on curves},
language = {eng},
number = {1},
pages = {129-142},
title = {Holomorphic triples of genus 0},
url = {http://eudml.org/doc/269439},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Stefano Pasotti
AU - Francesco Prantil
TI - Holomorphic triples of genus 0
JO - Open Mathematics
PY - 2008
VL - 6
IS - 1
SP - 129
EP - 142
AB - Here we study the relationship between the stability of coherent systems and the stability of holomorphic triples over a curve of arbitrary genus. Moreover we apply these results to study some properties and give some examples of holomorphic triples on the projective line.
LA - eng
KW - Holomorphic triples; coherent systems; vector bundles; projective line; epistability; coherent system; stable vector bundle; vector bundles on curves
UR - http://eudml.org/doc/269439
ER -

References

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  1. [1] Bradlow S.B., Daskalopoulos G.D., García-Prada O., Wentworth R., Stable augmented bundles over Riemann surfaces, Vector bundles in algebraic geometry (Durham 1993), London Math. Soc. Lecture Notes Ser., 1995, 208, 15–67 Zbl0827.14010
  2. [2] Bradlow S.B., García-Prada O., An application of coherent systems to a Brill-Noether problem, J. Reine Angew. Math., 2002, 551, 123–143 Zbl1014.14012
  3. [3] Bradlow S.B., García-Prada O., Stable triples equivariant bundles and dimensional reduction, Math. Ann., 1996, 304, 225–252 http://dx.doi.org/10.1007/BF01446292 Zbl0852.32016
  4. [4] Bradlow S.B., García-Prada O., Gothen P.B., Moduli spaces of holomorphic triples over compact Riemann surfaces, Math. Ann., 2004, 328, 299–351 http://dx.doi.org/10.1007/s00208-003-0484-z Zbl1041.32008
  5. [5] Bradlow S.B., García-Prada O., Gothen P.B., Homotopy groups of moduli spaces of representations, preprint available at http://arxiv.org/abs/math/0506444 v2 Zbl1165.14028
  6. [6] Bradlow S.B., García-Prada O., Mercat V., Muñoz V., Newstead P.E., On the geometry of moduli spaces of coherent systems on algebraic curves, preprint available at http://arxiv.org/abs/math/0407523 v5 Zbl1117.14034
  7. [7] Bradlow S.B., García-Prada O., Munoz V., Newstead P.E., Coherent systems and Brill-Noether theory, Internat. J. Math., 2003, 14, 683–733 http://dx.doi.org/10.1142/S0129167X03002009 Zbl1057.14041
  8. [8] Grothendieck A., Sur la classification des fibrés holomorphes sur la sphère de Riemann, Amer. J. Math., 1957, 79, 121–138 (in French) http://dx.doi.org/10.2307/2372388 Zbl0079.17001
  9. [9] Lange H., Newstead P.E., Coherent systems on elliptic curves, Internat. J. Math., 2005, 16, 787–805 http://dx.doi.org/10.1142/S0129167X05003090 Zbl1078.14045
  10. [10] Lange H., Newstead P.E., Coherent systems of genus 0, Internat. J. Math., 2004, 15, 409–424 http://dx.doi.org/10.1142/S0129167X04002326 Zbl1072.14039
  11. [11] Lange H., Newstead P.E., Coherent systems of genus 0 II Existence results for k ≥ 3, Internat. J. Math., 2007, 18, 363–393 http://dx.doi.org/10.1142/S0129167X07004072 Zbl1114.14022
  12. [12] Pasotti S., Prantil F., Holomorphic triples on elliptic curves, Results Math., 2007, 50, 227–239 http://dx.doi.org/10.1007/s00025-007-0248-2 
  13. [13] Schmitt A., A universal construction for the moduli spaces of decorated vector bundles, Habilitationsschrift, University of Essen, 2000 

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