Counting Surfaces Singular Along a Line in $P^3$

Shachar Carmeli; Lev Radzivilovsky

Counting Surfaces Singular Along a Line in $P^3$

Algebraic Geometry 2021-01-11 v3

Authors: Shachar Carmeli , Lev Radzivilovsky

Abstract

We enumerate the number of surfaces of degree $d$ in $P^3$ having a singular line of order $k$ , passing through $\delta$ generic points (where $\delta$ is the dimension of moduli space of such surfaces).

Keywords

algebraic surfaces del pezzo surfaces incidence geometry of points and lines

Cite

@article{arxiv.1812.02413,
  title  = {Counting Surfaces Singular Along a Line in $P^3$},
  author = {Shachar Carmeli and Lev Radzivilovsky},
  journal= {arXiv preprint arXiv:1812.02413},
  year   = {2021}
}

Comments

The second version fixes a computation mistake from the first version, example of cubic scrolls is added. The third version is grammar and style improvements

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