About the semiample cone of the symmetric product of a curve

作者：Artebani Michela^*; Laface Antonio; Pirola Gian Pietro

来源：International Mathematics Research Notices, 2017, (18): 5554-5576.

DOI：10.1093/imrn/rnw172

Let C be a smooth curve which is complete intersection of a quadric and a degree k > 2 surface in P-3 and let C-(2) be its second symmetric power. In this paper we study the finite generation of the extended canonical ring R(Delta, K) := circle plus(2)((a,b)is an element of Z) H-0(C-(2), a Delta + bK), where Delta is the image of the diagonal and K is the canonical divisor. In case the quadric is smooth, we show that R(Delta, K) is finitely generated if and only if the difference of the two g(1)k on C is torsion and then show that this holds on an analytically dense locus of the moduli space of such curves.

• 出版日期2017-9