Let C be a very general curve of genus g and let C(2) be its second symmetric product. This paper concerns the problem of describing the convex cone of all numerically effective R-divisors classes in the Néron–Severi space of C(2). In a recent work, Julius Ross improved the bounds on the nef cone of C(2) in the case of genus five. By using his techniques and by studying the gonality of the curves lying on C(2), we give new bounds on the nef cone of C(2) when C is a very general curve of genus 5 ≤ g ≤ 8.

Bastianelli, F. (2009). Remarks on the nef cone on symmetric products of curves. MANUSCRIPTA MATHEMATICA, 130(1), 113-120 [10.1007/s00229-009-0274-3].

Remarks on the nef cone on symmetric products of curves

BASTIANELLI, FRANCESCO
2009

Abstract

Let C be a very general curve of genus g and let C(2) be its second symmetric product. This paper concerns the problem of describing the convex cone of all numerically effective R-divisors classes in the Néron–Severi space of C(2). In a recent work, Julius Ross improved the bounds on the nef cone of C(2) in the case of genus five. By using his techniques and by studying the gonality of the curves lying on C(2), we give new bounds on the nef cone of C(2) when C is a very general curve of genus 5 ≤ g ≤ 8.
Articolo in rivista - Articolo scientifico
symmetric products of curves, ample cone, nef divisors
English
2009
130
1
113
120
open
Bastianelli, F. (2009). Remarks on the nef cone on symmetric products of curves. MANUSCRIPTA MATHEMATICA, 130(1), 113-120 [10.1007/s00229-009-0274-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/21034
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