On normal embedding of complex algebraic surfaces

TL;DR

This paper constructs examples of complex algebraic surfaces that cannot be embedded normally into complex algebraic sets, highlighting limitations in embedding properties of such surfaces.

Contribution

It provides explicit examples of complex algebraic surfaces that do not admit normal embeddings, advancing understanding of embedding limitations in complex algebraic geometry.

Findings

Existence of complex algebraic surfaces without normal embeddings

Examples demonstrate restrictions on embedding complex surfaces

Highlights differences between algebraic and semialgebraic embedding properties

Abstract

We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.