Non-algebraizable neighborhoods of curves

2024/07/29 by Maycol Falla Luza, Luza, Maycol Falla, Frank Loray +3 · 1 citation
Mathematics · #51M15 #57N40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2407.20206

openalex publication_date 2024/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide several families of compact complex curves embedded in smooth complex surfaces such that no neighborhood of the curve can be embedded in an algebraic surface. Different constructions are proposed, by patching neighborhoods of curves in projective surfaces, and blowing down exceptional curves. These constructions generalize examples recently given by S. Lvovski. One of our non algebraic argument is based on an extension theorem of S. Ivashkovich.

Cited by

• Neighborhoods of curves with a prescribed number of foliations

Related

• Neighborhoods of rational curves without functions
• Connections and restrictions to curves
• Topology of real algebraic curves near the non-singular tropical limit
• Embeddings of curves and surfaces
• Neighborhood of a rational curve with an ordinary cusp