A characterization of double covers of curves in terms of the ample cone of second symmetric product

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 $\le \frac{g-1}{8}$. This is a generalization of a result by Debarre.

13 pages, to appear in J. Pure App. Algebra