Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one

Takuro Abe

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arXiv · 2206.15059

Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one

Takuro Abe

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Abstract

We study a generalized version of Terao's famous addition theorem for free arrangements to the category of those with projective dimension one. Namely, we give a criterion to determine the algebraic structure of logarithmic derivation modules of the addition when the deletion and restrictions are free with a mild condition. Also, we introduce a class of divisionally SPOG arrangements whose SPOGness depends only on the intersection lattice like Terao's famous conjecture on combinatoriality of freeness.

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Takuro Abe. 2022-06-30. Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one. https://arxiv.org/abs/2206.15059

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