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Working paper

On Hurwitz--Severi numbers

Yurii Burman, Shapiro B.
For a point p in a complex projective plane and a triple (g,d,l) of non-negative integers we define a plane Hurwitz number of the Severi variety W_{g,d,l} consisting of all reduced irreducible plane curves of genus g and degree d+l having an l-fold node at p and at most ordinary nodes as singularities at the other points. In the cases d+l >= g+2 and d+2l >= g+2 > d+l we express the plane Hurwitz numbers via appropriate ordinary Hurwitz numbers. The remaining case d+2l<g+2 is still widely open.