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Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one
Abe, Takuro1
1 Rikkyo University Department of Mathematics 3-34-1 Nishi-Ikebukuro, Toshima-Ku 1718501, Tokyo Japan
Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 413-429.

We study a generalized version of Terao’s addition theorem for free arrangements to the category of those with projective dimension one. Namely, we give a formulation to determine the algebraic structure of the logarithmic derivation module of a hyperplane arrangement obtained by adding one hyperplane to a free arrangement under the assumption that the arrangement obtained by restricting onto that hyperplane is free too.

Also, we introduce a class of stair-strictly plus-one generated (SPOG) arrangements whose SPOGness depends only on the intersection lattice similar to the class of stair-free arrangements which satisfies Terao’s conjecture.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.340
Classification: 32S22, 52C35
Keywords: hyperplane arrangements, logarithmic derivation modules, free arrangements, SPOG arrangements, the addition-deletion theorems

Abe, Takuro 1

1 Rikkyo University Department of Mathematics 3-34-1 Nishi-Ikebukuro, Toshima-Ku 1718501, Tokyo Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Abe, Takuro. Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one. Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 413-429. doi : 10.5802/alco.340. https://alco.centre-mersenne.org/articles/10.5802/alco.340/

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