Curves with A_k-singularities on K3 surfaces
 
Andreas Leopold Knutsen (University of Bergen)



Let (S,H) be a general primitively polarized K3 surface. I will talk about a joint work with Concettina Galati, where we prove the existence of curves in the complete linear system |nH| with A_k-singularities and living in families of the "expected dimension". This generalizes results in the nodal case of Mumford for n=1 and
Chen for n>1. The proof is by degenerating the K3 surface to a union of rational normal scrolls and deform a higher order tacnode on a curve on the degerated surface.



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