Abstract:
For an algebraic curve that has only simplest singularities and only
rational irreducible components, the generalized Jacobian coincides
with the moduli variety of topologically trivial linear bundles whose
canonical compactification is a toric variety constructed from a
convex integer polytope. The vertices of this polytope are the simple
cycles in the one-dimensional rational homology space of the dual
graph of this curve. It is proved that for three-connected graphs the
simple cycle polytope uniquely determines the graph.
Bibliography: 4 titles.
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