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.

Revised:

Accepted:

Published online:

Keywords: hyperplane arrangements, logarithmic derivation modules, free arrangements, SPOG arrangements, the addition-deletion theorems

Abe, Takuro ^{1}

@article{ALCO_2024__7_2_413_0, author = {Abe, Takuro}, title = {Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one}, journal = {Algebraic Combinatorics}, pages = {413--429}, publisher = {The Combinatorics Consortium}, volume = {7}, number = {2}, year = {2024}, doi = {10.5802/alco.340}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.340/} }

TY - JOUR AU - Abe, Takuro TI - Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one JO - Algebraic Combinatorics PY - 2024 SP - 413 EP - 429 VL - 7 IS - 2 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.340/ DO - 10.5802/alco.340 LA - en ID - ALCO_2024__7_2_413_0 ER -

%0 Journal Article %A Abe, Takuro %T Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one %J Algebraic Combinatorics %D 2024 %P 413-429 %V 7 %N 2 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.340/ %R 10.5802/alco.340 %G en %F ALCO_2024__7_2_413_0

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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