JournalsrlmVol. 23, No. 3pp. 295–317

On the existence of curves with a triple point on a KK3 surface

  • Concettina Galati

    Università degli Studi della Calabria, Arcavacata di Rende (Cosenza), Italy
On the existence of curves with a triple point on a $K$3 surface cover
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Abstract

Let (S,H)(S,H) be a general primitively polarized K3K3 surface of genus p and let pa(nH)p_a(nH) be the arithmetic genus of nH.nH. We prove the existence in OS(nH)|\mathcal O_S(nH)| of curves with a triple point and AkA_k-singularities. In particular, we show the existence of curves of geometric genus gg in OS(nH)|\mathcal O_S(nH)| with a triple point and nodes as singularities and corresponding to regular points of their equisingular deformation locus, for every 1gpa(nH)31\leq g\leq p_a(nH)-3 and (p,n)(4,1).\neq (4,1). Our result is obtained by studying the versal deformation space of a non-planar quadruple point.

Cite this article

Concettina Galati, On the existence of curves with a triple point on a KK3 surface. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 23 (2012), no. 3, pp. 295–317

DOI 10.4171/RLM/629