Motives associated to sums of graphs

Details Motives associated to sums of graphs Motives associated to sums of graphs

2008-10-07

arxiv.org/abs/0810.1313v1

Mathematics

Algebraic Geometry

Scientific paper

The Feynman amplitude associated to a graph is a period of a certain motive. The sum of these motive classes over all connected graphs with no multiple edges or tadpoles and n vertices is defined in the Grothendieck ring of varieties. This sum is shown to lie in the subring generated by the affine line. It follows from work of Belkale and Brosnan that motives of individual graphs do not lie in this subring.

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