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The Brill–Noether curve and Prym-Tyurin varieties

Abstract

We prove that the Jacobian of a general curve C of genus \(g=2a+1\), with \(a\ge 2\), can be realized as a Prym-Tyurin variety for the Brill–Noether curve \(W^{1}_{a+2}(C)\). As consequence of this result we are able to compute the class of the sum of secant divisors of the curve C, embedded with a complete linear series \(g^{a-1}_{3a-2}\).

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Acknowledgments

I would like to thank to A. Beauville, C. Ciliberto, G. Farkas, E. Izadi, G.-P. Pirola, O. Serman and A. Verra for stimulating conversations. Research partially supported by the Sonderforschungsbereich 647 “Raum - Zeit - Materie”.

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Correspondence to Angela Ortega.

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Ortega, A. The Brill–Noether curve and Prym-Tyurin varieties. Math. Ann. 356, 809–817 (2013). https://doi.org/10.1007/s00208-012-0870-5

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Mathematics Subject Classification (1991)

  • 14H40