On the Singular Structure of Graph Hypersurfaces

Details On the Singular Structure of Graph Hypersurfaces On the Singular Structure of Graph Hypersurfaces

2010-04-29

arxiv.org/abs/1004.5166v2

Mathematics

Algebraic Geometry

49 pages

Scientific paper

We show that the singular loci of graph hypersurfaces correspond set-theoretically to their rank loci. The proof holds for all configuration hypersurfaces and depends only on linear algebra. To make the conclusion for the second graph hypersurface, we prove that the second graph polynomial is a configuration polynomial. The result indicates that there may be a fruitful interplay between the current research in graph hypersurfaces and Stratified Morse Theory.

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