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About the semiample cone of the symmetric product of a curve | | Michela Artebani
; Antonio Laface
; Gian Pietro Pirola
; | | Date: |
1 Feb 2015 | | Abstract: | Let $C$ be a smooth curve which is complete intersection of a quadric and a
degree $k>2$ surface in $mathbb{P}^3$ and let $C^{(2)}$ be its second
symmetric power. In this paper we study the finite generation of the extended
canonical ring $R(Delta,K) :=
igoplus_{(a,b)inmathbb{Z}^2}H^0(C^{(2)},aDelta+bK)$, where $Delta$ is the
image of the diagonal and $K$ is the canonical divisor. We first show that
$R(Delta,K)$ is finitely generated if and only if the difference of the two
$g_k^1$ on $C$ is torsion non-trivial and then show that this holds on an
analytically dense locus of the moduli space of such curves. | | Source: | arXiv, 1502.0298 | | Services: | Forum | Review | PDF | Favorites | |
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