Abstract
In this paper we characterize the irreducible curves lying in \(C^{(2)}\). We prove that a curve B has a degree one morphism to \(C^{(2)}\) with image a curve of degree d, with irreducible preimage in \(C\times C\), if and only if there exists an irreducible smooth curve D and morphisms from D to C and B, of degrees d and 2 respectively, forming a diagram which does not reduce.
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Acknowledgments
The author thanks Miguel Angel Barja and Joan Carles Naranjo for the multiple discussions and invaluable help on the development of this article. And the Universitat de Barcelona for the APIF grant and their hospitality afterwards. The author has been partially supported by the Proyecto de Investigación MTM2012-38122-C03-02.
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Sáez, M. Characterization of curves in \(C^{(2)}\) . Collect. Math. 67, 399–405 (2016). https://doi.org/10.1007/s13348-015-0147-x
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DOI: https://doi.org/10.1007/s13348-015-0147-x