Acta Mathematica Vietnamica

, Volume 38, Issue 4, pp 563–573 | Cite as

On the gonality sequence of smooth curves: normalizations of singular curves in a quadric surface

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Abstract

Let C be a smooth curve of genus g. For each positive integer r, the r-gonality d r (C) of C is the minimal integer t such that there is \(L\in \operatorname{Pic}^{t}(C)\) with h 0(C,L)=r+1. In this paper, for all g≥40805 we construct several examples of smooth curves C of genus g with d 3(C)/3<d 4(C)/4, i.e. for which a slope inequality fails.

Keywords

Gonality sequence Smooth curve 

Mathematics Subject Classification (2000)

14H45 14H50 
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Notes

Acknowledgements

I want to thank the referee for several extremely useful remarks (in this version Step (⋄) of the proof of Proposition 1 is due to the referee).

The author was partially supported by MIUR and GNSAGA of INdAM (Italy)

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2013

Authors and Affiliations

  1. 1.Dept. of MathematicsUniversity of TrentoTrentoItaly

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