  We introduce a new class of arrangements of hyperplanes, called (strictly)
plus-one generated arrangements, from algebraic point of view. Plus-one
generatedness is close to freeness, i.e., plus-one generated arrangements have
their logarithmic derivation modules generated by dimension plus one elements,
with relations containing one linear form coefficient. We show that strictly
plus-one generated arrangements can be obtained if we delete a hyperplane from
free arrangements. We show a relative freeness criterion in terms of plus-one
generatedness. In particular, for plane arrangements, we show that a free
arrangement is in fact surrounded by free or strictly plus-one generated
arrangements. We also give several applications.
