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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

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