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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Cocycles on tropical varieties via piecewise polynomials
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by Georges Francois PDF
Proc. Amer. Math. Soc. 141 (2013), 481-497 Request permission

Abstract:

We use piecewise polynomials to define tropical cocycles generalising the well-known notion of tropical Cartier divisors to higher codimensions. Groups of cocycles are tropical analogues of Chow cohomology groups. We also introduce an intersection product of cocycles with tropical cycles (the counterpart of the classical cap product) and prove that this gives rise to a Poincaré duality in some cases.
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Additional Information
  • Georges Francois
  • Affiliation: Fachbereich Mathematik, Technische Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
  • Email: gfrancois@email.lu
  • Received by editor(s): March 29, 2011
  • Received by editor(s) in revised form: July 5, 2011
  • Published electronically: June 22, 2012
  • Additional Notes: The author is supported by the Fonds National de la Recherche (FNR), Luxembourg.
  • Communicated by: Lev Borisov
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 481-497
  • MSC (2010): Primary 14T05; Secondary 14C17, 14F99
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11359-0
  • MathSciNet review: 2996952