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Non-surjective Gaussian maps for singular curves on K3 surfaces

  • Claudio Fontanari
  • Edoardo Sernesi
Article
  • 15 Downloads

Abstract

Let (SL) be a polarized K3 surface with \(\mathrm {Pic}(S) = \mathbb {Z}[L]\) and \(L\cdot L=2g-2\), let C be a nonsingular curve of genus \(g-1\) and let \(f:C\rightarrow S\) be such that \(f(C) \in \vert L \vert \). We prove that the Gaussian map \(\Phi _{\omega _C(-T)}\) 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 \(\widetilde{S}\) of S at x and a theorem of L’vovski.

Keywords

K3 surface Nodal curve Gaussian map Wahl map 

Mathematics Subject Classification

Primary 14J28 14H10 Secondary 14H51 

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Copyright information

© Universitat de Barcelona 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TrentoTrentoItaly
  2. 2.Dipartimento di Matematica e FisicaUniversità Roma TreRomeItaly

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