Detail Semistable reduction in characteristic zero Bibliografi Author: Karu, Kalle ; Abramovich, Dan (Advisor) Topik: MATHEMATICS Bahasa: (EN )    ISBN: 0-599-23545-4     Penerbit: Boston University     Tahun Terbit: 1999     Jenis: Theses - Dissertation Fulltext: 9923957.pdf (0.0B; 0 download) Abstract Let f: X → B be a family of varieties. We consider the problem of replacing the family f with a new family $f\prime :X\prime \to B\prime$ such that all fibers of f′ are as nice as possible. The correct definition of “as nice as possible” is given in terms of toric geometry, and a morphism f ′ satisfying it is called semistable. The semistable. reduction problem then asks to find a generically finite proper base change $B\prime \to B$ and a proper birational morphism $X\prime \to X\times BB\prime$ such that the induced morphism $f\prime :X\prime \to B\prime$ is semistable. Semistable reduction was proved by Kempf, Knudsen, Mumford and Saint-Donat in the case when the base B is a curve, and by de Jong in the case when the relative dimension of f is one. We extend these results by proving semistable. reduction for families of surfaces and three-folds, and a slightly weaker version of semistable. reduction for an arbitrary morphism. As an application of weak semistable, reduction, we show that, assuming the minimal model program in dimension n + 1, one can compactify the moduli space of n-dimensional nonsingular stable varieties with a given Hilbert function by adding a finite number of families of stable (singular) n-folds on the boundary. Opini Anda Klik untuk menuliskan opini Anda tentang koleksi ini! Lihat Sejarah Pengadaan  Konversi Metadata   Kembali

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