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

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.