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We develop the theory of associating moduli spaces with nice geometric properties to arbitrary Artin stacks generalizing Mumford's geometric invariant theory and tame stacks.
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Masaki Maruyama, Moduli of stable sheaves. I , J. Math. Kyoto Univ. 17
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Brian Conrad, Keel-mori theorem via stacks , http://www.math.lsa.umich.edu/~bdconrad/papers/coarsespace.pdf
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Brendan Hassett, Classical and minimal models of the moduli space of curves of genus two , Geometric methods in algebra and number theory, Progr. Math., vol. 235, Birkhäuser Boston, Boston, MA, 2005, pp. 169–192
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by same author, Finite generation of certain subrings , Proc. Amer. Math. Soc. 99
1987
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Friedrich Knop, Hanspeter Kraft, and Thierry Vust, The Picard group of a G G -variety , Algebraische Transformationsgruppen und Invariantentheorie, DMV Sem., vol. 13, Birkhäuser, Basel, 1989, pp. 77–87
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Hanspeter Kraft, G G -vector bundles and the linearization problem , Group actions and invariant theory (Montreal, PQ, 1988), CMS Conf. Proc., vol. 10, Amer. Math. Soc., Providence, RI, 1989, pp. 111–123
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Gerd Faltings and Ching-Li Chai, Degeneration of abelian varieties , Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 22, Springer-Verlag, Berlin, 1990, With an appendix by David Mumford
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David Schubert, A new compactification of the moduli space of curves , Compositio Math. 78
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Lucia Caporaso, A compactification of the universal Picard variety over the moduli space of stable curves , J. Amer. Math. Soc. 7
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D. Mumford, J. Fogarty, and F. Kirwan, Geometric invariant theory , third ed., Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)], vol. 34, Springer-Verlag, Berlin, 1994
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Angelo Vistoli, Grothendieck topologies, fibered categories and descent theory , Fundamental algebraic geometry, Math. Surveys Monogr., vol. 123, Amer. Math. Soc., Providence, RI, 2005, pp. 1–104
2005
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Brendan Hassett and Donghoon Hyeon, Log canonical models for the moduli space of curves: First divisorial contraction , math.AG/0607477 (2006)
2006
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Donghoon Hyeon and Yongnam Lee, Log minimal model program for the moduli space of stable curves of genus three , math.AG/0703093 (2007)
2007
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Donghoon Hyeon and Yongnam Lee, Stability of tri-canonical curves of genus two , Math. Ann. 337
2007
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Max Lieblich, Moduli of twisted sheaves , Duke Math. J. 138
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Margarida Melo, Compactified picard stacks over ℳ ¯ g \overline{\mathcal{M}}_{g} , math.AG/0710.3008 (2007)
2007
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Martin Olsson, Sheaves on Artin stacks , J. Reine Angew. Math. 603
2007
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David Rydh, Existence of quotients by finite groups and coarse moduli spaces , math.AG/0708.3333 (2007)
2007
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Dan Abramovich, Martin Olsson, and Angelo Vistoli, Tame stacks in positive characteristic , Ann. Inst. Fourier (Grenoble) 58
2008
Closest in time.
by same author, Log minimal model program for the moduli space of stable curves: The first flip , math.AG/0806.3444 (2008)
2008
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by same author, Noetherian approximation of algebraic spaces and stacks , in preparation (2008)
2008
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