The Local Structure of Compactified Jacobians: The Cographic Ring

Details The Local Structure of Compactified Jacobians: The Cographic Ring The Local Structure of Compactified Jacobians: The Cographic Ring

2011-02-13

arxiv.org/abs/1102.2547v1

Mathematics

Commutative Algebra

37 pages

Scientific paper

We study a certain toric face ring associated to a graph, called the
cographic toric face ring. It is defined in terms of the following equivalent
combinatorial structures: the poset of totally cyclic orientations, the
cographic arrangement of hyperplanes, and the Voronoi polytope. These rings
arise naturally in the local study of compactified Jacobians of nodal curves.

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