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

## TL;DR

This paper counts the number of degree d surfaces in projective 3-space with a singular line of order k passing through a specified number of generic points, contributing to enumerative geometry.

## Contribution

It provides a new enumeration formula for surfaces with a singular line of given order passing through generic points in P^3.

## Key findings

- Derived explicit counts for surfaces with singular lines of specified order.
- Extended enumerative techniques to include singular lines in P^3.
- Connected the count to the dimension of the moduli space.

## 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).