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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cocycles on tropical varieties via piecewise polynomials


Author: Georges Francois
Journal: Proc. Amer. Math. Soc. 141 (2013), 481-497
MSC (2010): Primary 14T05; Secondary 14C17, 14F99
Published electronically: June 22, 2012
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11359-0
PII: S 0002-9939(2012)11359-0
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.