Moduli Spaces and Related Topics | On Hurwitz-Severi numbers

Abstract：

For a point p in CP2 and a triple (g, d, l) of non-negative integers we define a Hurwitz–Severi number Hg,d,l as the number of generic 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, such that the projection of the curve from p has a prescribed set of local and remote tangents and lines passing through nodes. Under certain conditions we express the above Hurwitz-Severi numbers via appropriate Hurwitz numbers. Several questions will be posed.