Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Syzygies using vector bundles

Author: Montserrat Teixidor i Bigas
Journal: Trans. Amer. Math. Soc. 359 (2007), 897-908
MSC (2000): Primary 14H51, 14H15, 14M60
Published electronically: September 11, 2006
MathSciNet review: 2255200
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper studies syzygies of curves that have been embedded in projective space by line bundles of large degree. The proofs take advantage of the relationship between syzygies and spaces of section of vector bundles associated to the given line bundles.

References [Enhancements On Off] (What's this?)

  • [A] M. Aprodu, Green-Lazarsfeld gonality conjecture for a generic curve of odd genus, Inter. Math. Res. Not. 63, (2004), 3409-3416. MR 2098645 (2005k:14012)
  • [AV] M. Aprodu, C. Voisin, Green-Lazarsfeld conjecture for generic curves of large gonality, Comptes Rendus Ac. Scien. 36, (2003), 335-339.MR 1976314 (2004a:14033)
  • [B] D. Butler, Normal generation of vector bundles over a curve, J. Differential Geometry 39, (1994), 1-34. MR 1258911 (94k:14024)
  • [Eh] S. Ehbauer, Syzygies of points in projective space and applications, in ``Proceedings of the International Conference, Ravello 1992'', ed. by Orechia and Chiantini, Walter de Gruyter, 145-170.MR 1292482 (95h:13012)
  • [Ei] D. Eisenbud, The geometry of syzygies, Graduate Texts in Math., vol. 229, Springer, 2005. MR 2103875 (2005h:13021)
  • [G] M. Green, Koszul cohomology and the geometry of projective varieties, J. Diff. Geom. 19, (1984), 125-168. MR 0739785 (85e:14022)
  • [GL1] M. Green, R. Lazarsfeld, The non-vanishing of certain Koszul cohomology groups, J. Diff. Geom. 19, (1984), 168-171.
  • [GL2] M. Green, R. Lazarsfeld, On the projective normality of complete linear series on an algebraic curve, Invent. Math 83, (1986), 73-90. MR 0813583 (87g:14022)
  • [GL3] M. Green, R. Lazarsfeld, A simple proof of Petri's Theorem on canonical curves in ``Geometry Today, Giornate di Geometria, Roma 1984'', Birkhauser 1985, 129-142. MR 0895152 (88h:14038)
  • [L] R. Lazarsfeld, A sampling of vector bundle techniques in the study of linear series, in ``Lectures on Riemann Surfaces, Trieste 1987'', World Scient. Publ., 500-559. MR 1082360 (92f:14006)
  • [M] R. Miranda, Algebraic Curves and Riemann Surfaces, Grad. Studies in Math. 5, A.M.S. 1991. MR 1326604 (96f:14029)
  • [V] C. Voisin, Courbes tetragonales et cohomologie de Koszul, J. Reine Angew. Math. 387, (1988), 111-121. MR 0946352 (89e:14036)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14H51, 14H15, 14M60

Retrieve articles in all journals with MSC (2000): 14H51, 14H15, 14M60

Additional Information

Montserrat Teixidor i Bigas
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155

Received by editor(s): March 24, 2004
Received by editor(s) in revised form: January 7, 2005
Published electronically: September 11, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society