Tootfinder

Hyperbolicity of smooth logarithmic and orbifold pairs in $\mathbb{P}^n$
Clara D\'erand
https://arxiv.org/abs/2406.04069 https://…

Hyperbolicity of smooth logarithmic and orbifold pairs in $\mathbb{P}^n$
We derive a necessary and sufficient condition on a hyperplane arrangement in $\mathbb{P}^n$ for the associated logarithmic cotangent bundle to be ample modulo boundary. We extend this result to the orbifold setting and give some applications concerning hyperbolicity of pairs.

Vertex Representation of Hyperbolic Tensor Networks
Matej Mosko, Maria Polackova, Roman Krcmar, Andrej Gendiar
https://arxiv.org/abs/2406.03426 https://

Vertex Representation of Hyperbolic Tensor Networks
We propose a vertex representation of the tensor network (TN) in the anti-de Sitter space (AdS$_{2+0}$) that we model on a subset of hyperbolic lattices. The tensors form a network of regular $p$-sided polygons ($p>4$) with the coordination number four. The response to multi-state spin systems on the hyperbolic TN is analyzed for their entire parameter space. We show that entanglement entropy is sensitive to distinguish various hyperbolic geometries whereas other thermodynamic quantities are no…

This https://arxiv.org/abs/2401.07831 has been replaced.
link: https://scholar.google.com/scholar?q=a

Reduced polygons in the hyperbolic plane
For a hyperplane $H$ supporting a convex body $C$ in the hyperbolic space $\mathbb{H}^d$ we define the width of $C$ determined by $H$ as the distance between $H$ and a most distant ultraparallel hyperplane supporting $C$. The minimum width of $C$ over all supporting $H$ is called the thickness $Δ(C)$ of $C$. A convex body $R \subset \mathbb{H}^d$ is said to be reduced if $Δ(Z) < Δ(R)$ for every convex body $Z$ properly contained in $R$. We describe a class of reduced polygons in $\mathbb{H}^…

All crepant resolutions of hyperpolygon spaces via their Cox rings
Austin Hubbard
https://arxiv.org/abs/2406.04117 https://arxiv.org/…

All crepant resolutions of hyperpolygon spaces via their Cox rings
We construct and enumerate all crepant resolutions of hyperpolygon spaces, a family of conical symplectic singularities arising as Nakajima quiver varieties associated to a star-shaped quiver. We provide an explicit presentation of the Cox ring of any such crepant resolution. Using techniques developed by Arzhantsev-Derenthal-Hausen-Laface we construct all crepant resolutions of the hyperpolygon spaces, including those which are not projective over the singularity. We find that the number of cr…

This https://arxiv.org/abs/1106.3959 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

Quantum cohomology of twistor spaces and their Lagrangian submanifolds
We compute the classical and quantum cohomology rings of the twistor spaces of 6-dimensional hyperbolic manifolds and the eigenvalues of quantum multiplication by the first Chern class. Given a half-dimensional totally geodesic submanifold we associate, after Reznikov, a monotone Lagrangian submanifold of the twistor space. In the case of a 3-dimensional totally geodesic submanifold of a hyperbolic 6-manifold we compute the obstruction term $m_0$ in the Fukaya-Floer $A_{\infty}$-algebra of a Re…

Weighted Voronoi-Delaunay dual on polyhedral surfaces and its finiteness
Xiang Zhu
https://arxiv.org/abs/2406.03717 https://arxiv.org…

Weighted Voronoi-Delaunay dual on polyhedral surfaces and its finiteness
We aim to give a strict proof of the existence and uniqueness of the weighted Voronoi decomposition and the dual weighted Delaunay triangulation on Euclidean and hyperbolic polyhedral surface as well as hyperbolic surface with geodesic boundaries. Since the former definition of the Voronoi cell may not be simply connected, we slightly adjust the definition. Our proof is to construct an isotopic map instead of using the edge-flipping algorithm, which is a generalization of the one by Dyer et al.…

Hubbard and Heisenberg models on hyperbolic lattices -- Metal-insulator transitions, global antiferromagnetism and enhanced boundary fluctuations
Anika G\"otz, Gabriel Rein, Jo\~ao Carvalho In\'acio, Fakher F. Assaad
https://arxiv.org/abs/2406.03416

Hubbard and Heisenberg models on hyperbolic lattices -- Metal-insulator transitions, global antiferromagnetism and enhanced boundary fluctuations
We study the Hubbard and Heisenberg models on hyperbolic lattices with open boundary conditions by means of mean-field approximations, spin-wave theory and quantum Monte Carlo (QMC) simulations. For the Hubbard model we use the auxiliary-field approach and for Heisenberg systems the stochastic series expansion algorithm. We concentrate on bipartite lattices where the QMC simulations are free of the negative sign problem. The considered lattices are characterized by a Dirac like density of state…

This https://arxiv.org/abs/1903.05054 has been replaced.
link: https://scholar.google.com/scholar?q=a

Flexible Clustering with a Sparse Mixture of Generalized Hyperbolic Distributions
Robust clustering of high-dimensional data is an important topic because clusters in real datasets are often heavy-tailed and/or asymmetric. Traditional approaches to model-based clustering often fail for high dimensional data, e.g., due to the number of free covariance parameters. A parametrization of the component scale matrices for the mixture of generalized hyperbolic distributions is proposed. This parameterization includes a penalty term in the likelihood. An analytically feasible expecta…

L-shadowing lemma for the Cauchy equation
K. Lee, C. A. Morales
https://arxiv.org/abs/2406.03951 https://arxiv.org/pdf/2406.03951

L-shadowing lemma for the Cauchy equation
We prove that if the Cauchy problem $\dot{u}=Au$ in a Banach space is hyperbolic, then the problem has the L-shadowing property. Conversely, if the space is finite-dimensional and the L-shadowing property is satisfied, then the problem is hyperbolic. This generalizes a previous result by Ombach \cite{o, o1} for linear homeomorphisms. Some short applications are given.

This https://arxiv.org/abs/2404.13936 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A bound preserving cut discontinuous Galerkin method for one dimensional hyperbolic conservation laws
In this paper we present a family of high order cut finite element methods with bound preserving properties for hyperbolic conservation laws in one space dimension. The methods are based on the discontinuous Galerkin framework and use a regular background mesh, where interior boundaries are allowed to cut through the mesh arbitrarily. Our methods include ghost penalty stabilization to handle small cut elements and a new reconstruction of the approximation on macro-elements, which are local patc…