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
2009-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
