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

MathSciNet review:
2996952

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Abstract | References | Similar Articles | Additional Information

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

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.