Pith. sign in

REVIEW 3 cited by

Patchworking real algebraic varieties

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0611382 v1 pith:HRUDBTHH submitted 2006-11-13 math.AG

classification math.AG
keywords patchworkingalgebraicrealhypersurfacescombinatorialcurvesplaneauthor
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Hilbert's 16th problem for arrangements of curves on a surface

    math.AG 2026-06 unverdicted novelty 7.0 of 10

    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...

  2. Real Lagrangians in Calabi-Yau Threefolds

    math.AG 2019-08 accept novelty 7.0 of 10

    The connecting homomorphism in the Castaño-Bernard-Matessi exact sequence for real Lagrangians in Calabi-Yau threefolds equals squaring in the mirror, yielding explicit mod 2 Betti numbers.

  3. Generating Special Triangulations with Transformers

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Transformers generate new FRSTs of 4D reflexive polytopes across size ranges and self-improve by retraining on their own outputs.

Pith tools