Related papers: Jets of flat partial connections
In this note we examine a natural concept of a curve on a supermanifold and the subsequent notion of the jet of a curve. We then tackle the question of geometrically defining the higher order tangent bundles of a supermanifold. Finally we…
We study contact structures on smooth complex projective varieties with a simple normal crossing divisor, generalizing some well-known results concerning the non-logarithmic case. In particular, we describe the structure of elementary log…
Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.
Image-based jet analysis is built upon the jet image representation of jets that enables a direct connection between high energy physics and the fields of computer vision and deep learning. Through this connection, a wide array of new jet…
We give a general construction of triangulations starting from a walk in the quarter plane with small steps, which is a discrete version of the mating of trees. We use a special instance of this construction to give a bijection between maps…
We introduce the notion of integrable connections for a sheaf of differential graded algebras on a topological space. We then describe them in the finite locally projective setting, when the sheaf is either the de Rham complex of a formal…
We study the branched holomorphic projective structures on a compact Riemann surface $X$ with a fixed branching divisor $S\, =\, \sum_{i=1}^d x_i$, where $x_i \,\in\, X$ are distinct points. After defining branched ${\rm SO}(3,{\mathbb…
Each irreducible component of the first resonance variety of a hyperplane arrangement naturally determines a codimension one foliation on the ambient space. The superposition of these foliations define what we call the resonance web of the…
We give an elementary explicit construction of cell decomposition of the moduli space of projective structures on a two dimensional surface analogous to the decomposition of Penner/Strebel for moduli space of complex structures. The…
The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…
We construct the equivalent of the Godbillon-Vey class and its generalizations for regular foliations on super-manifolds. We interpret these classes as classes of foliated flat connections.
It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the…
We develop an intersection theory for a singular hemitian line bundle with positive curvature current on a smooth projective variety and irreducible curves on the variety. And we prove the existence of a natural rational fibration structure…
We provide supplements and open problems related to structure theorems for maximal rationally connected fibrations of certain positively curved projective varieties, including smooth projective varieties with semi-positive holomorphic…
This paper deals essentially with affine or projective transformations of Lie groups endowed with a flat left invariant affine or projective structure. These groups are called flat affine or flat projective Lie groups. Our main results…
Local connection forms provide a very useful tool for handling connections on principal bundles, because they ignore any complexities of the total space and, essentially, involve only two fundamental features of the structure group, namely…
A holomorphic foliation is defined as an integrable coherent subsheaf of the tangent sheaf. The structure of the leaves around a singularity is read off from the structure of the stalks. This was done by Baum when the dimension of the…
The aim of this work is to describe the set of fixed point free homeomorphisms of the plane under certain expansive conditions.
We consider local invariants of general connections (with torsion). The group of origin-preserving diffeomorphisms acts on a space of jets of general connections. Dimensions of moduli spaces of generic connections are calculated. Poincar\'e…
We give a simple analytic criterion which characterizes linearizable 1-codimensional webs. Then we give an invariant geometrical interpretation of it, in term of projective connection. We explain then how our approach allows to study…