As soon as one has a stability condition on the derived category (or an admissible subcategory) of coherent sheaves on a projective variety, it is natural to inquire about the nature of the moduli of stable objects of a fixed chern class and fixed stability condition. These moduli come with determinant line bundles that relate “wall-crossings” on the stability manifold to a minimal model program for moduli spaces. This has been studied in detail for many surfaces (and non-commutative K3 categories). In higher dimensions the situation is more complicated, but motivated by examples of Schmitt, Xia and Rezaee, we construct a family of stability conditions on projective space that converges to Gieseker stability (in an appropriate sense) and realizes all the interesting wall-crossings. This is joint work with Matteo Altavilla, Dapeng Mu and Marin Petkovic.