11 citations · 16 across the 7 of their papers we have counts for
8 papers
First Betti number of real Calabi-Yau hypersurfaces: examples
Diego Matessi, Arthur Renaudineau
Continuing the investigation of real Calabi-Yau hypersurfaces in toric varieties obtained by patchworking, we present a new theorem concerning the computation of their first Betti…
Mirror symmetry for tropical hypersurfaces and patchworking
Diego Matessi, Arthur Renaudineau
In the first part of the paper, we prove a mirror symmetry isomorphism between integral tropical homology groups of a pair of mirror tropical Calabi-Yau hypersurfaces. We then appl…
Real phase structures on tropical manifolds and patchworks in higher codimension
Johannes Rau, Arthur Renaudineau, Kris Shaw
This paper generalises the homeomorphism theorem behind Viro's combinatorial patchworking of hypersurfaces in toric varieties to arbitrary codimension using tropical geometry. We f…
Real phase structures on matroid fans and matroid orientations
Johannes Rau, Arthur Renaudineau, Kris Shaw
We introduce the notion of real phase structure on rational polyhedral fans in Euclidean space. Such a structure consists of an assignment of affine spaces over $\mathbb{Z}/2\mathb…
Patchworking the Log-critical locus of planar curves
Lionel Lang, Arthur Renaudineau
We establish a patchworking theorem à la Viro for the Log-critical locus of algebraic curves in . As an application, we prove the existence of projective curves o…
Lefschetz section theorems for tropical hypersurfaces
Charles Arnal, Arthur Renaudineau, Kristin Shaw
We establish variants of the Lefschetz hyperplane section theorem for the integral tropical homology groups of tropical hypersurfaces of toric varieties. It follows from these theo…
Bounding the Betti numbers of real hypersurfaces near the tropical limit
Arthur Renaudineau, Kristin Shaw
We prove a bound conjectured by Itenberg on the Betti numbers of real algebraic hypersurfaces near non-singular tropical limits. These bounds are given in terms of the Hodge number…
Tropical limit of log-inflection points for planar curves
Grigory Mikhalkin, Arthur Renaudineau
The paper describes behavior of log-inflection points of curves in under passing to the tropical limit. We show that such points accumulate by pairs at the midpo…