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Singularities with Gmaction and the log minimal model program for M g
, 2010
"... We give a precise formulation of the modularity principle for the log canonical models ..."
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We give a precise formulation of the modularity principle for the log canonical models
EXISTENCE OF GOOD MODULI SPACES WITH APPLICATIONS TO THE LOG MINIMAL PROGRAM FOR Mg,n
"... Abstract. We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the KeelMori theorem, which guarantees the existence of a coarse moduli space for a separated DeligneMumford stack. We apply this result to prove that ..."
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Cited by 2 (2 self)
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Abstract. We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the KeelMori theorem, which guarantees the existence of a coarse moduli space for a separated DeligneMumford stack. We apply this result to prove that the moduli stacksMg,n(α) parameterizing αstable curves introduced in [AFSv14] admit good moduli spaces. Contents
LOG MINIMAL MODEL PROGRAM FOR THE MODULI SPACE OF STABLE CURVES: THE SECOND FLIP
"... Abstract. We prove an existence theorem for good moduli spaces, and use it to construct the second flip in the log minimal model program for Mg. In fact, our methods give a uniform selfcontained construction of the first three steps of the log minimal model program for Mg and Mg,n. ..."
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Cited by 1 (1 self)
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Abstract. We prove an existence theorem for good moduli spaces, and use it to construct the second flip in the log minimal model program for Mg. In fact, our methods give a uniform selfcontained construction of the first three steps of the log minimal model program for Mg and Mg,n.
RECASTING RESULTS IN EQUIVARIANT GEOMETRY  AFFINE COSETS, OBSERVABLE SUBGROUPS AND EXISTENCE OF GOOD QUOTIENTS
, 2010
"... ..."
Flattening stratification and the stack of partial stabilizations of
"... prestable curves ..."
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A LUNAÉTALE SLICE THEOREM FOR ALGEBRAIC STACKS
"... Abstract. We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, isétalelocally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group. The proof uses an equivariant version of Artin's algebraiz ..."
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Abstract. We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, isétalelocally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group. The proof uses an equivariant version of Artin's algebraization theorem proved in the appendix. We provide numerous applications of the main theorems.
LOG MINIMAL MODEL PROGRAM FOR M g: THE SECOND FLIP
"... We prove an existence theorem for good moduli spaces, and use it to construct the second flip in the log minimal model program for M g. In fact, our methods give a uniform, selfcontained construction of the first three steps of the log minimal model program for M g and M g,n. ..."
Abstract
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We prove an existence theorem for good moduli spaces, and use it to construct the second flip in the log minimal model program for M g. In fact, our methods give a uniform, selfcontained construction of the first three steps of the log minimal model program for M g and M g,n.