Patchworking the Log-critical locus of planar curves

Lang, Lionel; Renaudineau, Arthur

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1515/crelle-2022-0054

Title :

Patchworking the Log-critical locus of planar curves

Author(s) :

Lang, Lionel [Auteur]
University of Gävle
Renaudineau, Arthur [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal für die reine und angewandte Mathematik

Pages :

115-143

Publisher :

Walter de Gruyter

Publication date :

2022-11-01

ISSN :

0075-4102

HAL domain(s) :

Mathématiques [math]/Mathématiques générales [math.GM]

English abstract : [en]

Abstract We establish a patchworking theorem à la Viro for the Log-critical locus of algebraic curves in ( ℂ ∗ ) 2 {(\mathbb{C}^{\ast})^{2}} . As an application, we prove the existence of projective curves of arbitrary ...
Show more >Abstract We establish a patchworking theorem à la Viro for the Log-critical locus of algebraic curves in ( ℂ ∗ ) 2 {(\mathbb{C}^{\ast})^{2}} . As an application, we prove the existence of projective curves of arbitrary degree with smooth connected Log-critical locus. To prove our patchworking theorem, we study the behaviour of Log-inflection points along families of curves defined by Viro polynomials. In particular, we prove a generalisation of a theorem of Mikhalkin and the second author on the tropical limit of Log-inflection points.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

2103.02576
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