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  • Title Page
  • Authorization Page
  • Signature Page
  • Dedication Page
  • Acknowledgements
  • Table of Contents
  • Abstract
  • Introduction
    • Background
    • Motivations and ideas
    • Summary of main results
    • Outline of the paper
    • Notations and Terminologies
  • Bridgeland stability conditions
    • Arcara-Bertram's construction
    • Logarithm Todd class
    • The Mukai bilinear form
    • Central charge in terms of the Mukai bilinear form
    • Maciocia's theorem on the structure of the walls
    • Duality induced by derived dual
  • Bayer-Macrì's nef line bundle theory
    • Construction of Bayer-Macrì line bundle
    • Computation by using Z
    • Derived dual and correspondent line bundles
    • Identification of Néron-Severi groups
  • Large volume limit and natural morphisms
    • The semistable objects for 20
    • Moduli space for 20
    • Trivial chamber, Simpson chamber, (dual) Gieseker chamber
    • Simpson wall, (dual) Uhlenbeck wall
    • Gieseker-Uhlenbeck morphism
    • Support morphism
    • Classical twisted Gieseker wall-chambers
  • Bayer-Macrì decomposition
    • Preliminary computation
    • Local Bayer-Macrì decomposition
      • Supported in dimension 0
      • Supported in dimension 1
      • Supported in dimension 2
    • Le Potier's construction of determinant line bundles
    • Global Bayer-Macrì decomposition
      • Supported in dimension 1
      • Supported in dimension 2
  • Bridgeland-Mori correspondence for geometric Bridgeland stability
    • Bridgeland-Mori correspondence for geometric Bridgeland stability conditions
    • A conjecture on Hilbert scheme of points by Arcara, Bertram, Coskun, Huizenga
    • A toy model: fibered surface over P1 with a section
  • Twisted Gieseker stability and the large volume limit
  • Bayer-Macrì decomposition on K3 surfaces by using ,
    • Computation by using
    • Bayer-Macrì decomposition on K3 surfaces
  • Divisors, cones and Mori dream spaces
    • Divisors and cones
    • Mori dream spaces
  • Bibliography
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