Zobrazeno 1 - 10
of 159
pro vyhledávání: '"Panov, Dmitri"'
Autor:
Panov, Dmitri, Tahar, Guillaume
In their solution to the orchard-planting problem, Green and Tao established a structure theorem which proves that in a line arrangement in the real projective plane with few double points, most lines are tangent to the dual curve of a cubic curve. W
Externí odkaz:
http://arxiv.org/abs/2409.01892
Autor:
Mondello, Gabriele, Panov, Dmitri
We analyse local features of the spaces of representations of the fundamental group of a punctured surface in $\mathrm{SU}_2$ equipped with a decoration, namely a choice of a logarithm of the representation at peripheral loops. Such decorated represe
Externí odkaz:
http://arxiv.org/abs/2305.07160
We discuss here the geometry of frieze patterns, and add a few words about Greek vases, molecular symmetry, and 2D crystallography. The work is written primarily for school students.
Comment: 18 pages, 15 figures (in Russian)
Comment: 18 pages, 15 figures (in Russian)
Externí odkaz:
http://arxiv.org/abs/2210.07953
Autor:
de Borbon, Martin, Panov, Dmitri
We show that general Dunkl connections on $\mathbb{C}^2$ do not preserve non-zero Hermitian forms. Our proof relies on recent understanding of the non-trivial topology of the moduli space of spherical tori with one conical point.
Comment: 37 pag
Comment: 37 pag
Externí odkaz:
http://arxiv.org/abs/2209.05958
Autor:
de Borbon, Martin, Panov, Dmitri
We use the Kobayashi-Hitchin correspondence for parabolic bundles to reprove the results of Troyanov and Luo-Tian regarding existence and uniqueness of conformal spherical metrics on the Riemann sphere with prescribed cone angles in the interval $(0,
Externí odkaz:
http://arxiv.org/abs/2109.10250
Autor:
de Borbon, Martin, Panov, Dmitri
Let $X$ be a complex manifold and let $g$ be a polyhedral metric on it inducing its topology. We say that $g$ is a polyhedral K\"ahler (PK) metric on $X$ if it is K\"ahler outside its singular set. The local geometry of PK metrics is modelled on PK c
Externí odkaz:
http://arxiv.org/abs/2106.13224
Publikováno v:
Geom. Topol. 27 (2023) 3619-3698
In this paper we determine the topology of the moduli space $\mathcal{MS}_{1,1}(\vartheta)$ of surfaces of genus one with a Riemannian metric of constant curvature $1$ and one conical point of angle $2\pi\vartheta$. In particular, for $\vartheta\in (
Externí odkaz:
http://arxiv.org/abs/2008.02772
Publikováno v:
Communications in Contemporary Mathematics, 24, (2022) N2, 1-68
The space of Lam\'e functions of order m is isomorphic to the space of pairs (elliptic curve, Abelian differential) where the differential has a single zero of order 2m at the origin and m double poles with vanishing residues. We describe the topolog
Externí odkaz:
http://arxiv.org/abs/2006.16837
Autor:
Lindsay, Nicholas, Panov, Dmitri
We show that there exist symplectic structures on a $\mathbb CP^1$-bundle over $\mathbb CP^2$ that do not admit a compatible K\"ahler structure. These symplectic structures were originally constructed by Tolman and they have a Hamiltonian $\mathbb T^
Externí odkaz:
http://arxiv.org/abs/1912.02785
Autor:
Fine, Joel, Panov, Dmitri
Let M be a compact oriented even-dimensional manifold. This note constructs a compact symplectic manifold S of the same dimension and a map f from S to M of strictly positive degree. The construction relies on two deep results: the first is a theorem
Externí odkaz:
http://arxiv.org/abs/1905.05671