Motives of graph hypersurfaces with torus operations

TL;DR

This paper explores conditions for graph hypersurfaces to admit algebraic torus actions, enabling the potential computation of their motives via fixed point analysis, advancing understanding in algebraic geometry and graph theory.

Contribution

It introduces criteria for torus actions on graph hypersurfaces and connects these to motive computations through fixed point loci analysis.

Findings

Identifies conditions for algebraic torus operations on graph hypersurfaces

Links torus actions to the computation of graph motives

Provides a framework for analyzing fixed points in singularity resolutions

Abstract

We investigate graph hypersurfaces and study conditions under which graph hypersurfaces admit algebraic torus operations. This leads in principle to a computation of graph motives using the theorem of Bialynicki-Birula, provided one knows the fixed point loci in a resolution of singularities.