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Mat. Sb., 2006, Volume 197, Number 8, Pages 3–16 (Mi msb1111)  

This article is cited in 3 scientific papers (total in 3 papers)

Discrete Torelli theorem

I. V. Artamkin

Steklov Mathematical Institute, Russian Academy of Sciences

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.

DOI: https://doi.org/10.4213/sm1111

Full text: PDF file (412 kB)
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English version:
Sbornik: Mathematics, 2006, 197:8, 1109–1120

Bibliographic databases:

UDC: 512.772
MSC: Primary 05C20, 14H60; Secondary 14D20
Received: 05.07.2005

Citation: I. V. Artamkin, “Discrete Torelli theorem”, Mat. Sb., 197:8 (2006), 3–16; Sb. Math., 197:8 (2006), 1109–1120

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Caporaso L., Viviani F., “Torelli theorem for graphs and tropical curves”, Duke Math. J., 153:1 (2010), 129–171  crossref  mathscinet  zmath  isi  elib
    2. Greene J.E., “Lattices, Graphs, and Conway Mutation”, Invent. Math., 192:3 (2013), 717–750  crossref  mathscinet  zmath  adsnasa  isi
    3. Greene J.E., Juhasz A., Lackenby M., “Alternating Links and Definite Surfaces”, Duke Math. J., 166:11 (2017), 2133–2151  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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