Classification Of Higher Dimensional Algebraic Varieties Compact Moduli Spaces Of Canonically Polarized Varieties
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Classification of Higher Dimensional Algebraic Varieties
Author: Christopher D. Hacon
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-02-02
Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.
Quasi-projective Moduli for Polarized Manifolds
Author: Eckart Viehweg
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
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.
The Geometry of Moduli Spaces of Sheaves
Author: Daniel Huybrechts
language: en
Publisher: Cambridge University Press
Release Date: 2010-05-27
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.