New combinatorial encoding (n,W,T) classifies topological types of transverse curves in surface arrangements, yielding complete classification for three lines plus cubic and partial for quartic via Bézout obstructions, Viro patchworking, and a new Julia library.
Patchworking real algebraic varieties
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Patchworking is a construction of a one-parameter family of real algebraic hypersurfaces. For sufficiently small positive values of the parameter, the hypersurfaces can be obtained by gluing of given hypersurfaces topologically. The author invented patchworking in 1979-81 and used it for constructing of real plane algebraic curves with complicated prescribed topology. In particular, it helped to complete isotopy classification of nonsingular plane projective real algebraic curves of degree 7. A special case of the patchworking, combinatorial patchworking, can be considered as Litvinov-Maslov quantization of a tropical variety. Due to its simplicity, combinatorial patchworking is better known than the general one. This paper is the original presentation of the patchworking, in its full generality.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
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Hilbert's 16th problem for arrangements of curves on a surface
New combinatorial encoding (n,W,T) classifies topological types of transverse curves in surface arrangements, yielding complete classification for three lines plus cubic and partial for quartic via Bézout obstructions, Viro patchworking, and a new Julia library.
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Generating Special Triangulations with Transformers
Transformers generate new FRSTs of 4D reflexive polytopes across size ranges and self-improve by retraining on their own outputs.