scholarly journals The topology of integrable differential forms near a singularity

1982 ◽  
Vol 55 (1) ◽  
pp. 5-35 ◽  
Author(s):  
César Camacho ◽  
Alcides Lins Neto
Keyword(s):  
Differential Forms ◽  
Integrable Differential Forms

scholarly journals Truncated Local Uniformization of Formal Integrable Differential Forms

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
F. Cano ◽  
M. Fernández-Duque
Keyword(s):  
Differential Forms ◽  
Newton Polygon ◽  
Codimension One ◽  
Inductive Procedure ◽  
Rank One ◽  
Local Uniformization ◽  
Rational Rank ◽  
Integrable Differential Forms

AbstractWe prove the existence of Local Uniformization for rational codimension one foliations along rational rank one valuations, in any ambient dimension. This result is consequence of the Truncated Local Uniformization of integrable formal differential 1-forms, that we also state and prove in the paper. Thanks to the truncated approach, we perform a classical inductive procedure, based both in the control of the Newton Polygon and in the possibility of avoiding accumulations of values, given by the existence of suitable Tschirnhausen transformations.

scholarly journals On polytopes and generalizations of the KLT relations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nikhil Kalyanapuram
Keyword(s):  
Scattering Amplitudes ◽  
Large Class ◽  
Moduli Space ◽  
Differential Forms ◽  
Natural Generalization ◽  
Intersection Theory ◽  
Hyperplane Arrangements ◽  
Number Of Solutions ◽  
Scalar Theories ◽  
Double Copy

Abstract We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT). To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on ℳ0, n — the moduli space of marked Riemann spheres — the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.

Hamiltonian differential forms over the divided powers algebra

1986 ◽  
Vol 41 (2) ◽  
pp. 205-206
Author(s):  
M I Kuznetsov ◽  
S A Kirillov
Keyword(s):  
Differential Forms ◽  
Divided Powers
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