• A
  • A
  • A
  • АБB
  • АБB
  • АБB
  • А
  • А
  • А
  • А
  • А
Обычная версия сайта

Статья

On Hurwitz--Severi numbers

Shapiro B., Yurii Burman.

For a point p of the complex projective plane and a triple (g,d,l) of non-negative integers  we define a Hurwitz--Severi number H(g,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 above Hurwitz--Severi numbers via appropriate  ordinary Hurwitz numbers. The remaining case d+2l < g+2 is still widely  open.