Let (S,L) be a polarized K3 surface with Pic(S)=Z[L] and L⋅L=2g−2, let C be a nonsingular curve of genus g−1 and let f:C→S be such that f(C)∈|L|. We prove that the Gaussian map ΦωC(−T) is non-surjective, where T is the degree two divisor over the singular point x of f(C). This generalizes a result of Kemeny with an entirely different proof. It uses the very ampleness of C on the blown-up surface S˜ of S at x and a theorem of L'vovski. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAM.
Non-surjective Gaussian maps for singular curves on K3 surfaces / Fontanari, Claudio; Sernesi, Edoardo. - In: COLLECTANEA MATHEMATICA. - ISSN 0010-0757. - 70:1(2019), pp. 107-115. [10.1007/s13348-018-0223-0]
Non-surjective Gaussian maps for singular curves on K3 surfaces
Claudio Fontanari;Edoardo Sernesi
2019-01-01
Abstract
Let (S,L) be a polarized K3 surface with Pic(S)=Z[L] and L⋅L=2g−2, let C be a nonsingular curve of genus g−1 and let f:C→S be such that f(C)∈|L|. We prove that the Gaussian map ΦωC(−T) is non-surjective, where T is the degree two divisor over the singular point x of f(C). This generalizes a result of Kemeny with an entirely different proof. It uses the very ampleness of C on the blown-up surface S˜ of S at x and a theorem of L'vovski. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAM.File | Dimensione | Formato | |
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