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A LOWER BOUND FOR THE GONALITY CONJECTURE

Part of: Cycles and subschemes Curves Commutative algebra: Homological methods

Published online by Cambridge University Press:  03 April 2017

Wouter Castryck
Wouter Castryck*
Affiliation:
Laboratoire Paul Painlevé, Université de Lille-1, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France Departement Elektrotechniek, KU Leuven and imec-Cosic, Kasteelpark Arenberg 10/2452, 3001 Leuven, Belgium email [email protected]
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Abstract

For every integer $k\geqslant 3$ we construct a $k$-gonal curve $C$ along with a very ample divisor of degree $2g+k-1$ (where $g$ is the genus of $C$) to which the vanishing statement from the Green–Lazarsfeld gonality conjecture does not apply.

MSC classification

Primary: 13D02: Syzygies, resolutions, complexes 14C20: Divisors, linear systems, invertible sheaves 14H45: Special curves and curves of low genus
Type
Research Article
Information
Mathematika , Volume 63 , Issue 2 , 2017 , pp. 561 - 563
Copyright
Copyright © University College London 2017 

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References

Castryck, W., Cools, F., Demeyer, J. and Lemmens, A., Computing graded Betti tables of toric surfaces. Preprint, 2016, arXiv:1606.08181.Google Scholar
Ein, L. and Lazarsfeld, R., The gonality conjecture on syzygies of algebraic curves of large degree. Publ. Math. Inst. Hautes Études Sci. 122(1) 2015, 301–313.Google Scholar
Farkas, G. and Kemeny, M., Linear syzygies of curves with prescribed gonality. Preprint, 2016, arXiv:1610.04424.Google Scholar
Green, M., Koszul cohomology and the geometry of projective varieties. J. Differential Geom. 19(1) 1984, 125–171.Google Scholar
Green, M. and Lazarsfeld, R., On the projective normality of complete linear series on an algebraic curve. Invent. Math. 83(1) 1986, 73–90.Google Scholar
Rathmann, J., An effective bound for the gonality conjecture. Preprint, 2016, arXiv:1604.06072.Google Scholar
Serrano, F., Extension of morphisms defined on a divisor. Math. Ann. 277(3) 1987, 395–413.CrossRefGoogle Scholar
Teixidor i Bigas, M., Syzygies using vector bundles. Trans. Amer. Math. Soc. 359(2) 2007, 897–908.CrossRefGoogle Scholar