A Non-Algebraic Patchwork

2007/01/09 by Benoît Bertrand, Bertrand, Benoit, Erwan Brugallé +1
Computer Science · Engineering · Mathematics · #14H50 #14J26 #14P25 #32Q65 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.math/0701246

openalex publication_date 2007/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Itenberg and Shustin's pseudoholomorphic curve patchworking is in principle more flexible than Viro's original algebraic one. It was natural to wonder if the former method allows one to construct non-algebraic objects. In this paper we construct the first examples of patchworked real pseudoholomorphic curves in Σ_n whose position with respect to the pencil of lines cannot be realised by any homologous real algebraic curve.

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