Let be a general primitively polarized surface of genus p and let be the arithmetic genus of We prove the existence in of curves with a triple point and -singularities. In particular, we show the existence of curves of geometric genus in with a triple point and nodes as singularities and corresponding to regular points of their equisingular deformation locus, for every and (p,n) Our result is obtained by studying the versal deformation space of a non-planar quadruple point.
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Concettina Galati, On the existence of curves with a triple point on a 3 surface. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 23 (2012), no. 3, pp. 295–317DOI 10.4171/RLM/629