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2005 Combinatorial duality and intersection product: A direct approach
Gottfried Barthel, Jean-Paul Brasselet, Karl-Heinz Fieseler, Ludger Kaup
Tohoku Math. J. (2) 57(2): 273-292 (2005). DOI: 10.2748/tmj/1119888340


The proof of the Combinatorial Hard Lefschetz Theorem for the "virtual'' intersection cohomology of a not necessarily rational polytopal fan as presented by Karu completely establishes Stanley's conjectures for the generalized $h$-vector of an arbitrary polytope. The main ingredients, Poincaré Duality and the Hard Lefschetz Theorem, rely on an intersection product. In its original constructions, given independently by Bressler and Lunts on the one hand, and by the authors of the present article on the other, there remained an apparent ambiguity. The recent solution of this problem by Bressler and Lunts uses the formalism of derived categories. The present article instead gives a straightforward approach to combinatorial duality and a natural intersection product, completely within the framework of elementary sheaf theory and commutative algebra, thus avoiding derived categories.


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Gottfried Barthel. Jean-Paul Brasselet. Karl-Heinz Fieseler. Ludger Kaup. "Combinatorial duality and intersection product: A direct approach." Tohoku Math. J. (2) 57 (2) 273 - 292, 2005.


Published: 2005
First available in Project Euclid: 27 June 2005

zbMATH: 1107.14017
MathSciNet: MR2137471
Digital Object Identifier: 10.2748/tmj/1119888340

Primary: 14F43
Secondary: 14M25, 52Bxx

Rights: Copyright © 2005 Tohoku University


Vol.57 • No. 2 • 2005
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