Let T be an algebraic torus acting on a smooth variety V. There are many ways to define a quotient out of this data. A geometric invariant theory (GIT) quotient depends, even topologically, on the choice of a line bundle on V. Another, more stable construction is to take a symplectic quotient of the cotangent bundle of V. I will define all of these quotients, and describe a sense in which the latter is like "all the GIT quotients at once". |
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