正常复合物的混合体积

Pub Date : 2024-06-04 DOI:10.1007/s00454-024-00662-w

Lauren Nowak, Patrick O’Melveny, Dustin Ross

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引用次数: 0

摘要

正态复数是简单扇形的正交截断。在本文中，我们发展了对正复数混合体积的研究。我们的主要结果是一个充分条件，它确保与给定扇形相关的正复数的混合体积满足亚历山德罗夫-芬切尔不等式。通过专门研究矩阵的伯格曼扇形，我们给出了作为正复数亚历山德罗夫-芬切尔不等式后果的希伦-罗塔-韦尔什猜想的新证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Mixed Volumes of Normal Complexes

Normal complexes are orthogonal truncations of simplicial fans. In this paper, we develop the study of mixed volumes for normal complexes. Our main result is a sufficiency condition that ensures when the mixed volumes of normal complexes associated to a given fan satisfy the Alexandrov–Fenchel inequalities. By specializing to Bergman fans of matroids, we give a new proof of the Heron–Rota–Welsh Conjecture as a consequence of the Alexandrov–Fenchel inequalities for normal complexes.

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