In the preprint http://arxiv.org/pdf/0812.0433.pdf, Kaveh and Khovanskii define an intersection index for an n-tuple of finite-dimensional spaces of rational functions on an irreducible n-dimensional complex algebraic variety. Among the properties of the intersection index they prove, there is an analog of Alexandrov-Fenchel inequality (Theorem 4.28 and Corollary 4.29).
Margaret Friedland
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