Related papers: Algebraic Stability for Skew Products

We study dynamical systems induced by birational automorphisms on smooth cubic surfaces defined over a number field $K$. In particular we are interested in the product of non-commuting birational Geiser involutions of the cubic surface. We…

We consider for two based graphs $G$ and $H$ the sequence of graphs $G_k$ given by the wedge sum of $G$ and $k$ copies of $H$. These graphs have an action of the symmetric group $\Sigma_k$ by permuting the $H$-summands. We show that the…

We consider small perturbations of expanding maps induced by skew-product mappings whose base dynamics are not invertible necessarily. Adopting a previously developed perturbative spectral approach, we show stability of the densities of the…

We prove a homological stability theorem for moduli spaces of high-dimensional, highly connected manifolds, with respect to forming the connected sum with the product of spheres $S^{p}\times S^{q}$, for $p < q < 2p - 2$. This result is…

Let k be an uncountable algebraically closed field and let Y be a smooth projective k-variety which does not admit a decomposition of the diagonal. We prove that Y is not stably birational to a very general hypersurface of any given degree…

We study the stable norm on the first homology of a closed, non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm…

We provide a systematic way to design computable bilinear forms which, on the class of subspaces $W^* \subseteq \mathcal{V}'$ that can be obtained by duality from a given finite dimensional subspace $W$ of an Hilbert space $\mathcal{V}$,…

Bohn, Faenza, Fiorini, Fisikopoulos, Macchia, and Pashkovich (2015) conjectured that 2-level polytopes cannot simultaneously have many vertices and many facets, namely, that the maximum of the product of the number of vertices and facets is…

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…

This paper explores the stability of Minkowski-type inequalities for hypersurfaces in warped product spaces. We establish a stability estimate that bounds the norm of the traceless second fundamental form of the hypersurface in terms of the…

Let $S$ be a semigroup and $X$ a Banach space. The functional equation $\phi (xyz)+ \phi (x) + \phi (y) + \phi (z) = \phi (xy) + \phi (yz) + \phi (xz)$ is said to be stable for the pair $(X, S)$ if and only if $f: S\to X$ satisfying $\|…

We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.

Given a variety over a number field, are its rational points potentially dense, i.e., does there exist a finite extension over which rational points are Zariski dense? We study the question of potential density for symmetric products of…

The goal of this paper is to extend the standard invariant-theoretic design, well-developed in the reductive case, to the setting of representation of certain non-reductive groups. This concerns the following notions and results: the…

We study properties of stable, strictly stable and locally outermost marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes possessing certain symmetries such as isometries, homotheties and conformal Killings. We first…

Given a general K3 surface S of degree 18, lattice theoretic considerations allow to predict the existence of an anti-symplectic birational involution $\phi$ of the Hilbert cube $S^{[3]}$. We describe this involution in terms of the Mukai…

In this paper we study the anti-integrable limit scenario of skew-product systems. We consider a generalization of such systems based on the Frenkel-Kontorova model, and prove the existence of orbits with any fibered rotation number in…

For a group $G$ of finite Kurosh rank and for some arbiratily free product decomposition of $G$, $G = H_1 \ast H_2 \ast ... \ast H_r \ast F_q$, where $F_q$ is a finitely generated free group, we can associate some (relative) outer space…

We study a family of birational maps of smooth affine quadric 3-folds, {over the complex numbers}, of the form $x_1x_4-x_2x_3=$ constant, which seems to have some (among many others) interesting/unexpected characters: a) they are…

We study the limits of inductive sequences (A_i,\phi_i) where each A_i is a direct sum of full matrix algebras over compact metric spaces and each partial map of \phi_i is diagonal. We give a new characterisation of simplicity for such…