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Sbornik: Mathematics, 2006, Volume 197, Issue 8, Pages 1109–1120
DOI: https://doi.org/10.1070/SM2006v197n08ABEH003790 (Mi sm1111) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Discrete Torelli theorem

I. V. Artamkin

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (219 kB) Citations (13)
References:
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DOI: https://doi.org/10.1070/SM2006v197n08ABEH003790
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.
Received: 05.07.2005
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 8, Pages 3–16
DOI: https://doi.org/10.4213/sm1111
Bibliographic databases:
UDC: 512.772
MSC: Primary 05C20, 14H60; Secondary 14D20
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:537
    Russian version PDF:364
    English version PDF:38
    References:47
    First page:2
     
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