Zobrazeno 1 - 10
of 34
pro vyhledávání: '"Renaudineau, Arthur"'
Autor:
Matessi, Diego, Renaudineau, Arthur
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 apply this isomorphism to prove that a primitive patchworking of a central
Externí odkaz:
http://arxiv.org/abs/2407.13611
This paper generalises the homeomorphism theorem behind Viro's combinatorial patchworking of hypersurfaces in toric varieties to arbitrary codimension using tropical geometry. We first define the patchwork of a polyhedral space equipped with a real p
Externí odkaz:
http://arxiv.org/abs/2310.08313
Publikováno v:
J. Lond. Math. Soc. 106.4 (2022) pp. 3687-3710
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 $\mathbb{Z}/2\mathbb{Z}$ to each top dimensional face of the fan subject to two condition
Externí odkaz:
http://arxiv.org/abs/2106.08728
Autor:
Lang, Lionel, Renaudineau, Arthur
We establish a patchworking theorem \`a la Viro for the Log-critical locus of algebraic curves in $(\mathbb{C}^*)^2$. As an application, we prove the existence of projective curves of arbitrary degree with smooth connected Log-critical locus. To prov
Externí odkaz:
http://arxiv.org/abs/2103.02576
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 theorems that the integral tropical homology groups of non-singular tropic
Externí odkaz:
http://arxiv.org/abs/1907.06420
Autor:
Renaudineau, Arthur, Shaw, Kristin
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 numbers of the complexification. To prove the conjecture we introduce a real
Externí odkaz:
http://arxiv.org/abs/1805.02030
The paper describes behavior of log-inflection points of curves in $(\mathbb{C}^*)^2$ under passing to the tropical limit. We show that such points accumulate by pairs at the midpoints of bounded edges in the limiting tropical curve. Log-inflection p
Externí odkaz:
http://arxiv.org/abs/1612.04083
Publikováno v:
Ãpijournal de Géométrie Algébrique, Volume 1 (September 1, 2017) epiga:2030
Haas' theorem describes all partchworkings of a given non-singular plane tropical curve $C$ giving rise to a maximal real algebraic curve. The space of such patchworkings is naturally a linear subspace $W_C$ of the $\mathbb{Z}/2\mathbb{Z}$-vector spa
Externí odkaz:
http://arxiv.org/abs/1609.01979
Autor:
Renaudineau, Arthur
In this text, we study Viro's conjecture and related problems for real algebraic surfaces in $(\mathbb{CP}^1)^3$. We construct a counter-example to Viro's conjecture in tridegree $(4,4,2)$ and a family of real algebraic surfaces of tridegree $(2k,2l,
Externí odkaz:
http://arxiv.org/abs/1511.02261
Autor:
Renaudineau, Arthur
We give a constructive proof using tropical modifications of the existence of a family of real algebraic plane curves with asymptotically maximal numbers of even ovals.
Comment: 20 pages, 20 figures
Comment: 20 pages, 20 figures
Externí odkaz:
http://arxiv.org/abs/1510.03196