Smoothness, semi-stability and alterations
A. J. De Jong (1996)
Publications Mathématiques de l'IHÉS
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A. J. De Jong (1996)
Publications Mathématiques de l'IHÉS
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Tom Graber, Joe Harris, Barry Mazur, Jason Starr (2005)
Annales scientifiques de l'École Normale Supérieure
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The main purpose of this paper is twofold. We first analyze in detail the meaningful geometric aspect of the method introduced in [12], concerning families of irreducible, nodal curves on a smooth, projective threefold X. This analysis gives some geometric interpretations not investigated in [12] and highlights several interesting connections with families of other singular geometric objects related to X and to other varieties. Then we use this method to study analogous problems for...