相关论文: Flat 3-webs of degree one on the projective plane

We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two--dimensional…

We prove that a weak $\mathbb{Q}$-Fano $3$-fold with terminal singularities has unobstructed deformations. By using this result and computing some invariants of a terminal singularity, we provide two results on global deformation of a weak…

We give evidence for a uniformization-type conjecture, that any algebraic variety can be altered into a variety endowed with a tower of smooth fibrations of relative dimension one.

We construct an example of a birational transformation of a rational threefold for which the first and second dynamical degrees coincide and are $>1$, but which does not preserve any holomorphic (singular) foliation. In particular, this…

In this paper, we first give a new simple proof to the elimination theorem of definite fold by homotopy for generic smooth maps of manifolds of dimension strictly greater than $2$ into the $2$--sphere or into the real projective plane. Our…

We propose the Legendrian web in a contact three manifold as a second order generalization of the planar web. An Abelian relation for a Legendrian web is analogously defined as an additive equation among the first integrals of its…

We construct infinite families of non-simple isotopy classes of links in overtwisted contact structures on $S^1$-bundles over surfaces. These examples include: (1) a pair of Legendrian links that are not Legendrian isotopic, but which are…

We show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some…

In this paper, we consider Legendre trajectories of trans-$S$-manifolds. We obtain curvature characterizations of these curves and give a classification theorem. We also investigate Legendre curves whose Frenet frame fields are linearly…

We present a MAPLE program for the explicit computation of the curvature of calibrated ordinary webs in codimension one in any dimension (recall that all planar webs are calibrated and ordinary). The vanishing of this curvature means the…

Codimension one webs are configurations of finitely many codimension one foliations in general position. Much of the classical theory evolved around the concept of abelian relation: a functional relation among the first integrals of the…

The results of paper [1] are generalized for vacuum type-III solutions with, in general, a non-vanishing cosmological constant Lambda. It is shown that all curvature invariants containing derivatives of the Weyl tensor vanish if a type-III…

In this paper the author provides a generalization of classical linkage, i.e. linkage by a complete intersection, in a different context. Namely she looks at residuals in the scheme theoretic intersection of a rational normal surface or…

We continue our study, initiated in an earlier article, of a class of rigid hypersurfaces in ${\mathbb C}^3$ that are 2-nondegenerate and uniformly Levi degenerate of rank 1, having zero CR-curvature. We drop the restrictive assumptions of…

The presented paper is devoted to study the curvature and torsion of slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non- Frenet slant curves (with null…

We discuss the duality in three dimensional quantum field theory at infrared limit. The starting point is to use a conjecture of a duality between the free fermion and the interacting scalar field theories at the Wilson-Fisher fixed point.…

In order to analytically capture and identify peculiarities in the electronic structure of silicene, Weaire-Thorpe(WT) model, a standard model for treating three-dimensional (3D) silicon, is applied to silicene with the buckled 2D…

We propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor…

In this paper we study holomorphic foliations on $\mathbb{P}^2$ with only one singular point. If the singularity has algebraic multiplicity one, we prove that the foliation has no invariant algebraic curve. We also present several examples…

Let $S$ be a nonsingular minimal complex projective surface of general type and the canonical map of $S$ is generically finite. Beauville showed that the geometric genus of the image of the canonical map is vanishing or equals the geometric…