MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations

@article{Bayer2014MMPFM,
  title={MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations},
  author={Arend Bayer and Emanuele Macr{\`i}},
  journal={Inventiones mathematicae},
  year={2014},
  volume={198},
  pages={505-590}
}
  • Arend Bayer, Emanuele Macrì
  • Published 2014
  • Mathematics
  • Inventiones mathematicae
  • We use wall-crossing with respect to Bridgeland stability conditions to systematically study the birational geometry of a moduli space $$M$$M of stable sheaves on a K3 surface $$X$$X: (a) We describe the nef cone, the movable cone, and the effective cone of $$M$$M in terms of the Mukai lattice of $$X$$X. (b) We establish a long-standing conjecture that predicts the existence of a birational Lagrangian fibration on $$M$$M whenever $$M$$M admits an integral divisor class $$D$$D of square zero… CONTINUE READING

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