scholarly journals Equivariant cohomology and equivariant intersection theory

1998 ◽  
pp. 1-37 ◽  
Author(s):  
Michel Brion
Keyword(s):  
Equivariant Cohomology ◽  
Intersection Theory ◽  
Equivariant Intersection Theory

Equivariant intersection theory

1998 ◽  
Vol 131 (3) ◽  
pp. 595-634 ◽  
Author(s):  
Dan Edidin ◽  
William Graham
Keyword(s):  
Intersection Theory ◽  
Equivariant Intersection Theory

scholarly journals The Chow Ring of the Stack of Hyperelliptic Curves of Odd Genus

2019 ◽  
Author(s):  
Andrea Di Lorenzo
Keyword(s):  
Hyperelliptic Curves ◽  
Intersection Theory ◽  
Chow Ring ◽  
Equivariant Intersection Theory

Abstract We find a new presentation of the stack of hyperelliptic curves of odd genus as a quotient stack and we use it to compute its integral Chow ring by means of equivariant intersection theory.

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

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

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.

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