Related papers: The Classification of Exceptional CDQL Webs on Com…
We aim to classify codimension 1 foliations $\mathscr{F}$ with canonical singularities and $\nu(K_{\mathscr{F}}) < 3$ on threefolds of general type. We prove a classification result for foliations satisfying these conditions and having…
We introduce the decomposition rank, a notion of covering dimension for nuclear C^*-algebras. The decomposition rank generalizes ordinary covering dimension and has nice permanence properties; in particular, it behaves well with respect to…
For $(n+1)$-webs by curves in an ambiant $n$-dimensional manifold, we first define a generalization of the well known Blaschke curvature of the dimension two, which vanishes iff the web has the maximum possible rank which is one. But,…
For $d$ ranging from 2 to 6, we prove that the web by conics naturally defined on any smooth del Pezzo surface of degree $d$ carries an interesting functional identity whose components all are a certain antisymmetric hyperlogarithm of…
The cosmic web consists of a complex configuration of voids, walls, filaments, and clusters, which formed under the gravitational collapse of Gaussian fluctuations. Understanding under what conditions these different structures emerge from…
We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct…
In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we…
Complex supermanifold structures being deformations of the exterior algebra of a holomorphic vector bundle, have been parametrized by orbits of a group on non-abelian cohomology by P. Green. For the case of odd dimension $4$ and $5$ an…
Let $(X,o)$ be a complex normal surface singularity. We fix one of its good resolutions $\widetilde{X}\to X$, an effective cycle $Z$ supported on the reduced exceptional curve, and any possible (first Chern) class $l'\in…
We study webs in quantum type $C$, focusing on the rank three case. We define a linear pivotal category $\mathbf{Web}(\mathfrak{sp}_6)$ diagrammatically by generators and relations, and conjecture that it is equivalent to the category…
An abelian variety defined over an algebraically closed field k of positive characteristic is supersingular if it is isogenous to a product of supersingular elliptic curves and is superspecial if it is isomorphic to a product of…
We define a complex connection on a real hypersurface of $\C^{n+1}$ which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in $\C^{n+1}$, $n\ge 2$, which are…
A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient…
The present paper is a continuation of [13], [14] of the authors. Specifically, the paper considers the MD5-foliations associated to connected and simply connected MD5-groups such that their Lie algebras have 4-dimensional commutative…
We study 3d $\mathcal{N}=2$ dualities arising from the compactification of 4d $\mathcal{N}=1$ $Usp(2 n)$ SQCD with two antisymmetric rank-two tensors and $D_{k+2}$-type superpotential, with odd $k$. The analysis is carried out by using…
We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for…
In this text, we investigate webs which can be associated to cluster algebras from the point of view of the abelian functional equations these webs carry, focusing on the polylogarithmic ones. We introduce a general notion of webs whose…
The paper deals with a modified Godbillon-Vey class defined by Losik for codimension-one foliations. This characteristic class takes values in the cohomology of the second order frame bundle over the leaf space of the foliation. The…
In this paper, we define, from a finite set E of functions, a family of holomorphic webs ${\cal W}(n;E)$ of codimension one in any dimension $ n $. We prove that it is sufficient to check a finite number of conditions for these webs to be…
We classify singular Enriques surfaces in characteristic two supporting a rank nine configuration of smooth rational curves. They come in one-dimensional families defined over the prime field, paralleling the situation in other…