Quasi-projective Moduli for Polarized Manifolds
Viehweg, Eckart
Produktnummer:
18b2d082c642c54e8ea66b7c102e279fbf
Autor: | Viehweg, Eckart |
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Themengebiete: | Algebraische Räume Birationale Geometrie Divisor Geometrische Invarianten-Theorie Grothendieck topology Moduli Schemata Moduli schemes Polarisierte Mannigfaltigkeiten Schema algebraic geometry |
Veröffentlichungsdatum: | 27.12.2011 |
EAN: | 9783642797477 |
Sprache: | Englisch |
Seitenzahl: | 320 |
Produktart: | Kartoniert / Broschiert |
Verlag: | Springer Berlin |
Produktinformationen "Quasi-projective Moduli for Polarized Manifolds"
The concept of moduli goes back to B. Riemann, who shows in [68] that the isomorphism class of a Riemann surface of genus 9 ~ 2 depends on 3g - 3 parameters, which he proposes to name "moduli". A precise formulation of global moduli problems in algebraic geometry, the definition of moduli schemes or of algebraic moduli spaces for curves and for certain higher dimensional manifolds have only been given recently (A. Grothendieck, D. Mumford, see [59]), as well as solutions in some cases. It is the aim of this monograph to present methods which allow over a field of characteristic zero to construct certain moduli schemes together with an ample sheaf. Our main source of inspiration is D. Mumford's "Geometric In variant Theory". We will recall the necessary tools from his book [59] and prove the "Hilbert-Mumford Criterion" and some modified version for the stability of points under group actions. As in [78], a careful study of positivity proper ties of direct image sheaves allows to use this criterion to construct moduli as quasi-projective schemes for canonically polarized manifolds and for polarized manifolds with a semi-ample canonical sheaf.

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