Combinatorial duality and intersection product: A direct approach
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概要
- 論文の詳細を見る
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, Poincare 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.
- 東北大学の論文
著者
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Fieseler Karl-heinz
Matematiska Institutionen Uppsala Universitet
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Barthel Gottfried
Fachbereich Mathematik und Statistik, Universitat Konstanz
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Brasselet Jean-Paul
IML-CNRS
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Kaup Ludger
Fachbereich Mathematik und Statistik, Universitat Konstanz
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Barthel Gottfried
Fachbereich Mathematik Und Statistik Universitat Konstanz
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Kaup Ludger
Fachbereich Mathematik Und Statistik Universitat Konstanz
関連論文
- Combinatorial duality and intersection product: A direct approach
- Combinatorial intersection cohomology for fans
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