• Corpus ID: 251643620

Vector Spaces of Generalized Euler Integrals

@inproceedings{Agostini2022VectorSO,
  title={Vector Spaces of Generalized Euler Integrals},
  author={Daniele Agostini and Claudia Fevola and Anna-Laura Sattelberger and Simon Telen},
  year={2022}
}
We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman integrals from particle physics, this has been investigated using tools from homological algebra and the theory of D -modules. We present an overview and uncover new relations between these approaches. We also provide new algorithmic tools. 

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References

SHOWING 1-10 OF 50 REFERENCES

AN ALGORITHM OF COMPUTING COHOMOLOGY INTERSECTION NUMBER OF HYPERGEOMETRIC INTEGRALS

Abstract We show that the cohomology intersection number of a twisted Gauss–Manin connection with regularization condition is a rational function. As an application, we obtain a new quadratic

Introduction to Compact Riemann Surfaces

The theory of Riemann surfaces is a classical field of mathematics where geometry and analysis play equally important roles. The purpose of these notes is to present some basic facts of this theory

Likelihood Degenerations

Computing all critical points of a monomial on a very affine variety is a fundamental task in algebraic statistics, particle physics and other fields. The number of critical points is known as the

Global Analysis of GG Systems

This paper deals with some analytic aspects of GG system introduced by I.M.Gelfand and M.I.Graev: We compute the dimension of the solution space of GG system over the field of functions meromorphic

On twisted de Rham cohomology

Abstract. Consider the complex of differential forms on an open affine subvariety U of AN with differential where d is the usual exterior derivative and ø is a fixed 1-form on U. For certain U and ø,

Scattering Amplitudes from Intersection Theory.

Pic Picard-Lefschetz theory is used to prove a new formula for intersection numbers of twisted cocycles associated with a given arrangement of hyperplanes, which become tree-level scattering amplitudes of quantum field theories in the Cachazo-He-Yuan formulation.

Computing cohomology intersection numbers of GKZ hypergeometric systems

In this review article, we report on some recent advances on the computational aspects of cohomology intersection numbers of GKZ systems developed in \cite{GM}, \cite{MH}, \cite{MT} and \cite{MT2}.

D-Modules and Holonomic Functions

This lecture notes address the more general case when the coefficients are polynomials, and focuses on left ideals, or D-ideals, which represent holonomic functions in several variables by the linear differential equations they satisfy.

Feynman integrals and intersection theory

A bstractWe introduce the tools of intersection theory to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis. In order to illustrate this technique, we

Critical points and number of master integrals

A bstractWe consider the question about the number of master integrals for a multiloop Feynman diagram. We show that, for a given set of denominators, this number is totally determined by the