• 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. 
[PDF] Semantic Reader
2 Citations
Highly Influential Citations
1
Background Citations
1
Methods Citations
2

Figures from this paper

2 Citations

Twisted cohomology and likelihood ideals

A likelihood function on a smooth very affine variety gives rise to a twisted de Rham complex. We show how its top cohomology vector space degenerates to the coordinate ring of the critical points…

FeynGKZ: a Mathematica package for solving Feynman integrals using GKZ hypergeometric systems

In the Lee-Pomeransky representation, Feynman integrals can be identified as a sub-set of Euler-Mellin integrals, which are known to satisfy Gel ' fand-Kapranov-Zelevinsky (GKZ) system of partial…

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

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.

Constructive D-Module Theory with Singular

Several algorithms in computational D-module theory are overviewed together with the theoretical background as well as the implementation in the computer algebra system Singular, and a novel way to compute the Bernstein–Sato polynomial for an affine variety algorithmically is addressed.

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…

Zero loci of Bernstein-Sato ideals-II

We have recently proved a precise relation between Bernstein-Sato ideals of collections of polynomials and monodromy of generalized nearby cycles. In this article we extend this result to other…