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We study a generalized version of Terao's famous addition theorem for freearrangements to the category of those with projective dimension one. Namely, wegive a criterion to determine the algebraic structure of logarithmic derivationmodules of the addition when the deletion and restrictions are free with a mildcondition. Also, we introduce a class of divisionally SPOG arrangements whoseSPOGness depends only on the intersection lattice like Terao's famousconjecture on combinatoriality of freeness.

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