|4:00 pm Tuesday, August 30, 2011|
Algebraic Geometry Seminar : When is a scheme a quotient of a smooth scheme by a finite group?
Anton Geraschenko (Caltech) in HB 227
If a scheme X is a quotient of a smooth scheme by a finite group, it has quotient singularities---that is, it is _locally_ a quotient by a finite group. In this talk, we will see that the converse is true if X is quasi-projective and is known to be a quotient by a torus (e.g. X a simplicial toric variety). Though the proof is stack-theoretic, the construction of a smooth scheme U and finite group G so that X=U/G can be made explicit purely scheme-theoretically. To illustrate the construction, I'll produce a smooth variety U with an action of G=Z/2 so that U/G is the blow-up of P(1,1,2) at a smooth point. This example is interesting because even though U/G is toric, U cannot be taken to be toric.Host Department: Rice University-Mathematics
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