Reading Seminar in Algebraic Geometry: Peize Liu (UMass)

We begin with a review of slope stability as a prototype, introducing the stability function and the Harder–Narasimhan filtration. We then discuss two equivalent definitions of Bridgeland stability conditions, one in terms of hearts and the other in terms of slicings. The main goal of the talk is to understand the celebrated Bridgeland deformation theorem, and to state the general existence theorem for projective schemes. If time permits, I will also discuss the Bridgeland moduli spaces of stable objects.