On complete degenerations of surfaces with ordinary singularities in $\mathbb P^3$

TL;DR

This paper explores whether surfaces with ordinary singularities in projective 3-space can degenerate into arrangements of planes in general position, addressing a fundamental question in algebraic geometry.

Contribution

It provides new insights into the existence and construction of degenerations of surfaces with ordinary singularities into plane arrangements.

Findings

Identifies conditions for such degenerations to exist

Constructs explicit examples of degenerations

Clarifies the relationship between surface singularities and plane arrangements

Abstract

We investigate the problem of existence of degenerations of surfaces in $\mathbb P^3$ with ordinary singularities into plane arrangements in general position.