Let C be a smooth curve which is complete intersection of a quadric and a degree k > 2 surface in P3 and let C(2) be its second symmetric power. In this paper we study the finite generation of the extended canonical ring (R(,K) where is the image of the diagonal and K is the canonical divisor. In case the quadric is smooth, we show that R(,K) is finitely generated if and only if the difference of the two g1 k on C is torsion and then show that this holds on an analytically dense locus of the moduli space of such curves.
About the semiample cone of the symmetric product of a curve
PIROLA, GIAN PIETRO
2017-01-01
Abstract
Let C be a smooth curve which is complete intersection of a quadric and a degree k > 2 surface in P3 and let C(2) be its second symmetric power. In this paper we study the finite generation of the extended canonical ring (R(,K) where is the image of the diagonal and K is the canonical divisor. In case the quadric is smooth, we show that R(,K) is finitely generated if and only if the difference of the two g1 k on C is torsion and then show that this holds on an analytically dense locus of the moduli space of such curves.File in questo prodotto:
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