This paper classifies Poisson structures with the reduced simple normal crossing divisor on a product of Fano varieties of Picard number 1. The characterization of even-dimensional projective spaces from the viewpoint of Poisson structures is given by Lima and Pereira. In this paper, we generalize the characterization of projective spaces to any dimension.

中文翻译：

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Fano产品上的SNC对数辛结构

本文对皮卡德数为1的Fano乘积的具有简化的简单正态正交除数的Poisson结构进行分类。从Poisson结构的角度出发，偶数投影空间的特征由Lima和Pereira给出。在本文中，我们将投影空间的特征概括为任意维度。