On nodal deformations of singular surfaces in $\mathbb P^3$

TL;DR

This paper investigates how singular surfaces in projective 3-space can be deformed at their nodes, focusing on cases with isolated high-multiplicity singularities and line singularities.

Contribution

It provides new insights into the deformation behavior of singular surfaces with specific types of singularities in projective space.

Findings

Characterization of nodal deformations for surfaces with isolated singularities

Analysis of deformations along lines with ordinary singularities

Conditions under which deformations preserve or smooth singularities

Abstract

In this paper we study nodal deformations of singular surfaces $S\subset \mathbb P^3$. In particular we consider the case in which $S$ has an isolated singularity of multiplicity $m$ and the case in which $S$ has only ordinary singularities along a line.