Intersection Theory on Arithmetic Surfaces

1992 ◽  
pp. 228-268
Author(s):  
Ulrich Stuhler
Keyword(s):  
Intersection Theory ◽  
Arithmetic Surfaces

Line bundles on arithmetic surfaces and intersection theory

1996 ◽  
Vol 91 (1) ◽  
pp. 103-119
Author(s):  
Jörg Jahnel
Keyword(s):  
Intersection Theory ◽  
Line Bundles ◽  
Arithmetic Surfaces

scholarly journals Homotopical intersection theory I

2007 ◽  
Vol 11 (2) ◽  
pp. 939-977 ◽  
Author(s):  
John R Klein ◽  
E Bruce Williams
Keyword(s):  
Intersection Theory

Intersection theory and Hilbert function

2011 ◽  
Vol 45 (4) ◽  
pp. 305-315
Author(s):  
A. G. Khovanskii
Keyword(s):  
Hilbert Function ◽  
Intersection Theory

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.

scholarly journals Correction to: Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials

2021 ◽  
Author(s):  
Dawei Chen ◽  
Martin Möller ◽  
Adrien Sauvaget ◽  
Don Zagier
Keyword(s):  
Moduli Spaces ◽  
Intersection Theory ◽  
Abelian Differentials

A Correction to this paper has been published: https://doi.org/10.1007/s00222-020-00969-4

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