Abstract
Let X be a K3 surface and L be an ample line bundle on it. In this article, we will give an alternative and elementary proof of Lelli-Chiesa’s theorem in the case of \(r= 2\). More precisely, we will prove that under certain conditions the second co-ordinate of the gonality sequence is constant along the smooth curves in the linear system |L|. Using Lelli-Chiesa’s theorem for \(r \ge 3\), we also extend Lelli-Chiesa’s theorem in the case of \(r= 2\) in weaker condition.
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Acknowledgements
The author would like to thank Prof. A. J. Parameswaran for many useful discussions. He would also like to thank Prof. Ciliberto and Prof. P. Newstead for valuable comments and for pointing out the work done in this direction. He also thanks Krishanu Dan for a careful reading of the article.
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Communicating Editor: D S Nagaraj
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Pal, S. An elementary proof of Lelli-Chiesa’s theorem on constancy of second coordinate of gonality sequence. Proc Math Sci 132, 25 (2022). https://doi.org/10.1007/s12044-022-00677-4
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DOI: https://doi.org/10.1007/s12044-022-00677-4