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 pas...
Abstract The degeneration of Hodge structures is related to how a smooth projective variety degenerate. And it provides a Hodge-theoretic perspective to compactify moduli spaces. In this talk, I will focus on a particular degeneration of cubic hypersurfaces and study the associated limiting mixed Hodge structure. It generalizes some results in Radu Laza’s and Brendan Hassett’s works on cubic ...