On syzygies of Mori fiber spaces
Yang He
Source abstract
Abstract We introduce central models and elementary syzygies of Mori fiber spaces as a generalization of Sarkisov links and elementary relations of Sarkisov links. We generalize the (weak) Sarkisov program using central models and elementary syzygies. We construct a contractible CW complex such that there is a one‐to‐one correspondence between its cells and central models, and derive from this CW complex a long exact sequence of ‐modules and a spectral sequence converging to the discrete homology of the birational automorphism group . As an application, we partially compute the Schur multipliers of the Cremona group of rank 2, that is, .
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