Intersection theory, characteristic classes, and algebro-geometric Feynman rules
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
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