| Quasi-Projective Moduli for Polarized Manifolds Softcover Repri Edition Contributor(s): Viehweg, Eckart (Author) |
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ISBN: 3642797474 ISBN-13: 9783642797477 Publisher: Springer OUR PRICE: $132.99 Product Type: Paperback - Other Formats Published: December 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Algebraic - Mathematics | Mathematical Analysis |
| Dewey: 516.35 |
| Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a |
| Physical Information: 0.69" H x 6.14" W x 9.21" (1.03 lbs) 320 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |