Related papers: Tissus alg\'ebriques exceptionnels

A question of B. Teissier, inspired by a previous problem of R. Thom, asks whether for any germ of complex analytic hypersurface there exists a germ of complex algebraic hypersurface with the same topological type. Up to now only the case…

We study dimension theory for the $C^*$-algebras of row-finite $k$-graphs with no sources. We establish that strong aperiodicity - the higher-rank analogue of condition (K) - for a $k$-graph is necessary and sufficient for the associated…

Let r >= s >= 0 be integers and G be an r-graph. The higher inclusion matrix M_s^r(G) is a {0,1}-matrix with rows indexed by the edges of G and columns indexed by the subsets of V(G) of size s: the entry corresponding to an edge e and a…

We introduce two classes of algebras coming from partial triangulations of marked surfaces. The first one, called frozen algebra of a partial triangulation, is generally of infinite rank and contains frozen Jacobian algebras of…

An evolution algebra corresponds to a quadratic matrix $A$ of structural constants. It is known the equivalence between nil, right nilpotent evolution algebras and evolution algebras which are defined by upper triangular matrices $A$. We…

Many well-studied problems in extremal combinatorics deal with the maximum possible size of a family of objects in which every pair of objects satisfies a given restriction. One problem of this type was recently raised by Alon, Gujgiczer,…

Assuming the abundance conjecture in dimension $d$, we establish a non-algebraicity criterion of foliations: any log canonical foliation of rank $\le d$ with $\nu\neq\kappa$ is not algebraically integrable, answering question of…

Let $EG_r(n,k)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph with no Berge cycles of length $k$ or longer. In the first part of this work, we have found exact values of $EG_r(n,k)$ and described the structure…

For a smooth projective toric variety of Picard rank two we classify all exceptional sequences of invertible sheaves which have maximal length. In particular, we prove that unlike non-maximal sequences, they (a) remain exceptional under…

We introduce a new ``Winding Number Conjecture'' about maps from the $(d-1)$-skeleton of the $((d+1)(q-1))$-simplex into $\real^d$. This conjecture is equivalent to the Topological Tverberg Theorem. Furthermore, many statements about the…

The quasi-filiform Lie algebras of nonzero rank are described. The classifications of filiform and quasi-filiform naturally graded algebras are corrected.

We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree $n>2$ up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The…

We prove (without exceptions) the existence of irredundant tensor decompositions with the number of addenda equal to rank $+1$. We also discuss the existence of decompositions with more than the tensor rank terms, which are concise, while…

Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes…

Let $d$ be a positive integer. A finite group is called $d$-maximal if it can be generated by precisely $d$ elements, while its proper subgroups have smaller generating sets. For $d\in\{1,2\}$, the $d$-maximal groups have been classified up…

A work of Sorensen is rewritten here to include nontrivial types at the infinite places. This extends results of K. Ribet and R. Taylor on level-raising for algebraic modular forms on D^{\times}, where D is a definite quaternion algebra…

By arithmeticity and superrigidity, a commensurability class of lattices in a higher rank Lie group is defined by a unique algebraic group over a unique number subfield of $\mathbb{R}$ or $\mathbb{C}$. We prove an adelic version of…

For any d-web by curves in an ambiant n-dimensional manifold, we define a tautological connection on some associated bundle, whose curvature vanishes iff the web has a maximal (n-1)-rank. As an application we recover, with the help of a…

We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…

We investigate the question: when is a higher-rank graph C*-algebra approximately finite dimensional? We prove that the absence of an appropriate higher-rank analogue of a cycle is necessary. We show that it is not in general sufficient,…