PoS - Proceedings of Science
Volume 383 - MathemAmplitudes 2019: Intersection Theory & Feynman Integrals (MA2019) - Session 1: Hypergeometric Functions and Intersection Theory
Intersection theory, characteristic classes, and algebro-geometric Feynman rules
P. Aluffi* and M. Marcolli
Full text: pdf
Published on: February 15, 2022
We review the basic definitions in Fulton-MacPherson Intersection Theory and discuss
a theory of `characteristic classes' for arbitrary algebraic varieties, based on this
intersection theory. We also discuss a class of graph invariants motivated by
amplitude computations in quantum field theory. These `abstract Feynman rules'
are obtained by studying suitable invariants of hypersurfaces defined by the
Kirchhoff-Tutte-Symanzik polynomials of graphs. We review a `motivic' version
of these abstract Feynman rules, and describe a counterpart obtained by
intersection-theoretic techniques.
DOI: https://doi.org/10.22323/1.383.0012
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