The weighted projective superspace with weights +1, -1 and an analog of the Fubini--Study form

As a by-product of our work on super Pl\"ucker embedding, we came to the notion of a weighted projective superspace P+₁, -₁ (V W) with weights +1, -1. The construction is not in itself super and makes sense in ordinary (purely even) framework. Unlike the familiar weighted projective spaces with positive weights, the (super) space P+₁, -₁ (V W) is a smooth (super) manifold. We describe its structure and show that it possesses an analog of the Fubini--Study form.