Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Douai, Antoine"'
Autor:
Douai, Antoine
We study the interplay between Sabbah's mixed Hodge structure for regular functions and Ehrhart theory for polytopes. To this end, we analyze the properties of the Poincar\'e polynomial of the Hodge filtration of this mixed Hodge structure.
Comm
Comm
Externí odkaz:
http://arxiv.org/abs/2006.13669
Autor:
Douai, Antoine
We discuss the distribution of the spectrum at infinity of a convenient and nondegenerate Laurent polynomial (singularity side) and the distribution of the Newton spectrum of a polytope (Ehrhart theory side). To this end, we study a hard Lefschetz pr
Externí odkaz:
http://arxiv.org/abs/1910.02697
Autor:
Douai, Antoine
Gathering different results from singularity theory, geometry and combinatorics, we show that the spectrum at infinity of a tame Laurent polynomial counts lattice points in polytopes and we deduce an effective algorithm in order to compute the Ehrhar
Externí odkaz:
http://arxiv.org/abs/1811.07724
Autor:
Douai, Antoine
We define the toric Newton spectrum of a polynomial and we give some applications in singularity theory, combinatorics and mirror symmetry.
Comment: Minor changes
Comment: Minor changes
Externí odkaz:
http://arxiv.org/abs/1810.03901
Autor:
Douai, Antoine
Given a convex polytope, we define its geometric spectrum, a stacky version of Batyrev's stringy E-functions, and we prove a stacky version of a formula of Libgober and Wood about the E-polynomial of a smooth projective variety. As an application, we
Externí odkaz:
http://arxiv.org/abs/1603.08693
Autor:
Douai, Antoine
We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a good framew
Externí odkaz:
http://arxiv.org/abs/1203.5920
Autor:
Douai, Antoine, Mann, Etienne
We first describe a canonical mirror partner (B-model) of the small quantum orbifold cohomology of weighted projective spaces (A-model) in the framework of differential equations: we attach to the A-model (resp. B-model) a D-module on the torus and w
Externí odkaz:
http://arxiv.org/abs/0909.4063
Autor:
Douai, Antoine
We give examples of families of Frobenius type structures on the punctured plane and we study their limits at the boundary. We then discuss the existence of a limit Frobenius manifold. We also give an example of a logarithmic Frobenius manifold.
Externí odkaz:
http://arxiv.org/abs/0806.2011
Autor:
Douai, Antoine
Publikováno v:
Math. Z., vol 261, No 3, 2009, p. 625-648
We show that it makes sense to speak of THE Frobenius manifold attached to a convenient and nondegenerate Laurent polynomial
Comment: 24 pages
Comment: 24 pages
Externí odkaz:
http://arxiv.org/abs/0709.0186
Autor:
Douai, Antoine
We explain how to construct a Frobenius structure on the parameter space of the universal unfolding of a Laurent polynomial using a result of C. Hertling and Y. Manin. This new approach greatly simplifies the (classic) one used in the paper "Gauss-Ma
Externí odkaz:
http://arxiv.org/abs/math/0510437