Severi dimensions for unicuspidal curves

q-Floor Diagrams computing Refined Severi Degrees for Plane Curves

The Severi degree is the degree of the Severi variety parametrizing plane curves of degree d with δ nodes. Recently, Göttsche and Shende gave two refinements of Severi degrees, polynomials in a variable q, which are conjecturally equal, for large d. At q = 1, one of the refinements, the relative Severi degree, specializes to the (non-relative) Severi degree. We give a combinatorial description ...

Neron-severi Group for Torus Quasi Bundles over Curves

Linear Sections of the Severi Variety and Moduli of Curves

We study the Severi variety Vd,g of plane curves of degree d and geometric genus g. Corresponding to every such variety, there is a one-parameter family of genus g stable curves whose numerical invariants we compute. Building on the work of Caporaso and Harris, we derive a recursive formula for the degrees of the Hodge bundle on the families in question. For d large enough, these families induc...

Classification of Rational Unicuspidal Projective Curves Whose Singularities Have One Puiseux Pair

It is a very old and interesting open problem to characterize those collections of embedded topological types of local plane curve singularities which may appear as singularities of a projective plane curve C of degree d. (We invite the reader to consult the articles of Fenske, Flenner, Orevkov, Tono, Zaidenberg, Yoshihara, and the references therein, for recent developments.) The goal of the p...

Triangulations and Severi Varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as...