Stable maps of curves.
Coleman, Robert F. (2003)
Documenta Mathematica
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Coleman, Robert F. (2003)
Documenta Mathematica
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Lucia Caporaso, Filippo Viviani (2011)
Journal of the European Mathematical Society
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We study the Torelli morphism from the moduli space of stable curves to the moduli space of principally polarized stable semi-abelic pairs. We give two characterizations of its fibers, describe its injectivity locus, and give a sharp upper bound on the cardinality of finite fibers. We also bound the dimension of infinite fibers.
Siegfried Bosch, Werner Lütkebohmert (1985)
Mathematische Annalen
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Masami Fujimori (2003)
Bulletin de la Société Mathématique de France
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We show in detail that the category of general Roth systems or the category of semi-stable systems of linear inequalities of slope zero is a neutral Tannakian category. On the way, we present a new proof of the semi-stability of the tensor product of semi-stable systems. The proof is based on a numerical criterion for a system of linear inequalities to be semi-stable.
David Schubert (1991)
Compositio Mathematica
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Paul L. Strong (1975)
Colloquium Mathematicae
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Siegfried Bosch (1983-1984)
Groupe de travail d'analyse ultramétrique
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T. Noiri (1979)
Matematički Vesnik
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Atsushi Moriwaki (1996)
Journal für die reine und angewandte Mathematik
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Byunghan Kim, A. Pillay (2001)
Fundamenta Mathematicae
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We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory T has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.
Fumio Sakai (1980)
Mathematische Annalen
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V. Popa (1979)
Matematički Vesnik
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José A. Alvarez, Teresa Alvarez, Manuel González (1989)
Extracta Mathematicae
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