2016/04/23 by Yurii Burman, Boris Shapiro, Burman, Yurii +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Primary 14H50 #secondary 14H30
paper · pdf · doi:10.48550/arxiv.1604.06935
openalex publication_date 2016/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a point p∈ CP2 and a triple (g,d,ℓ) of non-negative integers we define a \em Hurwitz--Severi number \mathfrak 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. In the cases d+ℓ≥ g+2 and d+2ℓ ≥ g+2 > d+ℓ we express the Hurwitz--Severi numbers via appropriate ordinary Hurwitz numbers. The remaining case d+2ℓ