离散混合体积与Hodge-Deligne数
Discrete Mixed Volume and Hodge-Deligne Numbers
摘要：
推广著名的伯恩斯坦-库什尼连科定理，霍凡斯基在1978年证明了一个组合公式的算术亏格的紧致化一般完整的交叉家庭的格多面体。最近，一个类似的组合公式，称为离散混合体积，介绍了Bihan和证明是非负的。Khovanskii在他的论文中明确的脚注，我们解释这个不变量作为（motivic）算术亏格的非紧通用完整的交叉相关联的家庭的格多面体。
英文摘要：
Generalizing the famous Bernstein-Kushnirenko Theorem, Khovanskii proved in 1978 a combinatorial formula for the arithmetic genus of the compactification of a generic complete intersection associated to a family of lattice polytopes. Recently, an analogous combinatorial formula, called the discrete mixed volume, was introduced by Bihan and shown to be nonnegative. By making a footnote of Khovanskii in his paper explicit, we interpret this invariant as the (motivic) arithmetic genus of the non-compact generic complete intersection associated to the family of lattice polytopes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
