Related papers: Transversality for Holomorphic Supercurves

We prove that any graph of multicurves satisfying certain natural properties is either hyperbolic, relatively hyperbolic, or thick. Further, this geometric characterization is determined by the set of subsurfaces that intersect every vertex…

Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their…

We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an $SU(3)\times Spin(6+n)$ structure within…

Based on the fact that projective monomial curves in the plane are complete intersections, we give an effective inductive method for creating infinitely many monomial curves in the projective $n$-space that are set theoretic complete…

In this paper, we extend a result of Schwick concerning normality and sharing values in one complex variable for families of holomorphic curves taking values in $\mathbb{P}^n$. We consider wandering moving hyperplanes (i.e., depending on…

In this paper, we extend our result in [3] to hypersurfaces of any smooth projective variety $Y$. Precisely we let $X_0$ be a generic hypersurface of $Y$ and $c_0:\mathbf P^1\to X_0$ be a generic birational morphism to its image, i.e.…

The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…

We show that mapping class groups associated to all types of real algebraic curves are virtual duality groups. We also deduce some results about the orbifold homotopy groups of the moduli spaces of real algebraic curves. We achieve these…

We study the normal map for plane projective curves, i.e., the map associating to every regular point of the curve the normal line at the point in the dual space. We first observe that the normal map is always birational and then we use…

On the transversals of a subgroup of a group, using the binary operation of the group, structural mappings are defined. Based on these mappings, the notion of the hypergroup over the group is introduced, which generalizes the notion of the…

A theorem of Picard's type is proved for entire holomorphic mappings into complex projective varieties. This theorem has local character in the sense that the existence of Julia directions can be proved under a natural additional…

In generalized complex geometry, we revisit linear subspaces and submanifolds that have an induced generalized complex structure. We give an expression of the induced structure that allows us to deduce a smoothness criteria, we dualize the…

Given a smooth cubic hypersurface $X$ over a finite field of characteristic greater than 3 and two generic points on $X$, we use a function field analogue of the Hardy-Littlewood circle method to obtain an asymptotic formula for the number…

Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the…

We consider hyperbolic toral automorphisms which are reversible with respect to a linear area-preserving involution. We will prove that within this context reversibility is linked to a generalized Pell equation whose solutions we will…

Linear-nonlinear transforms are interesting in vision science because they are key in modeling a number of perceptual experiences such as color, motion or spatial texture. Here we first show that a number of issues in vision may be…

In this paper, we discuss the generalizations of exact supersymmetries present in the supersymmetrized sigma models. These generalizations are made by making the supersymmetric transformation parameter field-dependent. Remarkably, the…

We study curvature-adapted submanifolds of general symmetric spaces. We generalize Cartan's theorem for isoparametric hypersurfaces of spheres and Wang's classification of isoparametric Hopf hypersurfaces in complex projective spaces to any…

Generalizing the well-known Shafarevich hyperbolicity conjecture, it has been conjectured by Viehweg that a quasi-projective manifold that admits a generically finite morphism to the moduli stack of canonically polarized varieties is…

On a compact manifold with boundary, the map consisting of the scalar curvature in the interior and the mean curvature on the boundary is a local surjection at generic metrics. We prove that this result may be localized to compact…