### Compactifications of moduli spaces in real algebraic geometry.

R. Silhol (1992)

Inventiones mathematicae

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R. Silhol (1992)

Inventiones mathematicae

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Kapranov, M. (1998)

Documenta Mathematica

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Frans Oort (1974)

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F. Catanese (1989)

Inventiones mathematicae

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Herbert Popp (1973)

Inventiones mathematicae

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D. Groisser (1990)

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Fabrizio Catanese (1991)

Inventiones mathematicae

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Jarod Alper (2013)

Annales de l’institut Fourier

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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.

T. Figiel (1976)

Studia Mathematica

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G. Trautmann, Rosa María Miró-Roig (1994)

Mathematische Zeitschrift

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Jun Li (1994)

Inventiones mathematicae

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Marius van der Put (2011)

Banach Center Publications

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This paper is a sequel to [vdP-Sa] and [vdP]. The two classes of differential modules (0,-,3/2) and (-,-,3), related to PII, are interpreted as fine moduli spaces. It is shown that these moduli spaces coincide with the Okamoto-Painlevé spaces for the given parameters. The geometry of the moduli spaces leads to a proof of the Painlevé property for PII in standard form and in the Flaschka-Newell form. The Bäcklund transformations, the rational solutions and the Riccati solutions for PII...