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

2008/04/21 by Kungho Chan, Chan, Kungho
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.0804.3286

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

openalex publication_date 2008/04/21 · arxiv created 2008/05/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• New constructions of nef classes on self-products of curves
• Seshadri constants on symmetric products of curves
• Double covers of curves on Nikulin surfaces
• Pencils of double coverings of curves
• Effective cone of the blow up of the symmetric product of a curve