Related papers: Self-affine sets with fibered tangents

Affine schemes can be understood as objects of the opposite of the category of commutative and unital algebras. Similarly, $\mathscr{P}$-affine schemes can be defined as objects of the opposite of the category of algebras over an operad…

We study the fixed point sets of holomorphic self-maps of a bounded domain in ${\Bbb C}^n$. Specifically we investigate the least number of fixed points in general position in the domain that forces any automorphism (or endomorphism) to be…

This paper concerns the local study of analytic constrained differential systems (or impasse systems) of the form $A(x)\dot{x} = F(x)$, $x\in\mathbb{R}^{2}$, where $F$ is a vector field and $A$ is a matrix valued function. Using techniques…

We study composed map germs with respect to their local fibrations. Under most general conditions, inspired by the tameness condition that was introduced recently, we prove the existence of singular tube fibrations, and we determine the…

We classify compact K\"ahler manifolds with semi-positive holomorphic bisectional and big tangent bundles. We also classify compact complex surfaces with semi-positive tangent bundles and compact complex $3$-folds of the form $P(T^*X)$…

In this paper we study the connectedness of the fibers of integrable systems that extend complexity one $T$-spaces with proper moment maps, assuming that every tall singular point is non-degenerate. Our main result states that if there are…

Given $A\in\Omega_n,$ the $n^2$-dimensional spectral unit ball, we show that $B$ is a "generalized" tangent vector at $A$ to an entire curve in $\Omega_n$ if and only if $B$ is in the tangent cone $C_A$ to the isospectral variety at $A.$ In…

We study families of plane algebraic curves sharing the same set of foci. We reformulate confocality via a focal map on equiclassical families and analyze its fibers using deformation theory.

We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for…

In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle…

Let (X,d,p) be a pointed metric space. A pretangent space to X at p is a metric space consisting of some equivalence classes of convergent to p sequences (x_n), x_n \in X, whose degree of convergence is comparable with a given scaling…

Given a null-cobordant oriented framed link $L$ in a closed oriented $3$--manifold $M$, we determine those links in $M \setminus L$ which can be realized as the singular point set of a generic map $M \to \mathbb{R}^2$ that has $L$ as an…

We extend Falconer's 1988 landmark result on the dimensions of self-affine fractals to encompass the dimensions of their projections, showing furthermore that their families of exceptional projections contain algebraic varieties which are…

In this paper we describe the structure of the tangent cone of a numerical semigroup ring $A=k[[S]] \subseteq k[[t]]$ with multiplicity $e$ (as a module over the Noether normalization determined by the fiber cone of the ideal generated by…

We effectively bound T-singularities on non-rational projective surfaces with an arbitrary amount of T-singularities and ample canonical class. This fully generalizes the previous work for the case of one singularity, and illustrates the…

In this paper we introduce a local-refinement procedure to investigate finite t-stabilities on a triangulated category, and show a direct sufficient condition for a finite t-stability to be finite finest. We classify all finite finest…

We study the different rates of escape of points under iteration by holomorphic self-maps of $\mathbb C^*=\mathbb C\setminus\{ 0\}$ for which both 0 and $\infty$ are essential singularities. Using annular covering lemmas we construct…

Here is an English summary of the abstract: This research investigates a geometric dynamical mechanism within a specific class of domains that contain a fixed convex core. By using a radial structure that links the boundaries of the core…

Two finitely generated groups have the same set of finite quotients if and only if their profinite completions are isomorphic. Consider the map which sends (the isomorphism class of) an S-arithmetic group to (the isomorphism class of) its…

In this short note we prove that in many cases the failure of a variety to be separably rationally connected is caused by the instability of the tangent sheaf (if there are no other obvious reasons). A simple application of the results…