Let (S,H) be a general primitively polarized K3 surface. We prove the existence of irreducible curves in ∣OS(nH)∣ with Ak-singularities and corresponding to regular points of the equisingular deformation locus. Our result is optimal for n=1. As a corollary, we get the existence of irreducible curves in ∣OS(nH)∣ of geometric genus g≥1 with a cusp and nodes or a simple tacnode and nodes. We obtain our result by studying the versal deformation family of the m-tacnode. Moreover, using results on Brill-Noether theory of curves on K3 surfaces, we provide a regularity condition for families of curves with only Ak-singularities in ∣OS(nH)∣.
On the existence of curves with A_k -singularities on K3 surfaces / Galati, Concettina; Knutsen, A. L.. - In: MATHEMATICAL RESEARCH LETTERS. - ISSN 1073-2780. - 21:5(2014), pp. 1069-1109.
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Titolo: | On the existence of curves with A_k -singularities on K3 surfaces |
Autori: | |
Data di pubblicazione: | 2014 |
Rivista: | |
Citazione: | On the existence of curves with A_k -singularities on K3 surfaces / Galati, Concettina; Knutsen, A. L.. - In: MATHEMATICAL RESEARCH LETTERS. - ISSN 1073-2780. - 21:5(2014), pp. 1069-1109. |
Handle: | http://hdl.handle.net/20.500.11770/140507 |
Appare nelle tipologie: | 1.1 Articolo in rivista |