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Abstract

In this thesis, we study non-commutative projective schemes whose associated graded algebras are finite over their centers. We construct symmetric obstruction theories for their moduli spaces of stable sheaves in the Calabi–Yau-3 case. This allows us to define Donaldson–Thomas (DT) type deformation invariants. As an application, we study the quantum Fermat quintic threefold which is the quintic threefold in a quantum projective space. We give an explicit description of its local models in terms of quivers with potential. We then give a full computation of its degree zero DT invariants.