Abstract
We investigate the nef cone spanned by the diagonal and the fibre classes of second symmetric product of a curve of genus g . This 2-dimensional nef cone gives a characterization of double covers of curves of genus ≤ g − 1 8 . This is a generalization of a result by Debarre [Olivier Debarre, Seshadri constants of abelian varieties, in: The Fano Conference, Univ. Torino, Turin, 2004, pp. 379–394, Proposition 8].
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