Moduli Theory and Classification Theory of Algebraic Varieties
Author: H. Popp
Publisher: Springer
Published: 2006-11-15
Total Pages: 196
ISBN-13: 3540370315
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Classification of Higher Dimensional Algebraic Varieties
Author: Christopher D. Hacon
Publisher: Springer Science & Business Media
Published: 2011-02-02
Total Pages: 206
ISBN-13: 3034602901
DOWNLOAD EBOOKHigher 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.
Classification Theory of Algebraic Varieties and Compact Complex Spaces
Author: K. Ueno
Publisher: Springer
Published: 2006-11-15
Total Pages: 296
ISBN-13: 3540374159
DOWNLOAD EBOOKAlgebraic Geometry
Author: Robin Hartshorne
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 511
ISBN-13: 1475738498
DOWNLOAD EBOOKAn introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
An Introduction to Invariants and Moduli
Author: Shigeru Mukai
Publisher: Cambridge University Press
Published: 2003-09-08
Total Pages: 528
ISBN-13: 9780521809061
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The Geometry of Moduli Spaces of Sheaves
Author: Daniel Huybrechts
Publisher: Cambridge University Press
Published: 2010-05-27
Total Pages: 345
ISBN-13: 1139485822
DOWNLOAD EBOOKThis 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.
An Introduction to Families, Deformations and Moduli
Author: Thiruvalloor E. Venkata Balaji
Publisher: Universitätsverlag Göttingen
Published: 2010
Total Pages: 241
ISBN-13: 3941875329
DOWNLOAD EBOOKModuli Theory is one of those areas of Mathematics that has fascinated minds from classical to modern times. This has been so because it reveals beautiful Geometry naturally hidden in questions involving classification of geometric objects and because of the profound use of the methods of several areas of Mathematics like Algebra, Number Theory, Topology and Analysis to achieve this revelation. A study of Moduli Theory would therefore give senior undergraduate and graduate students an integrated view of Mathematics. The present book is a humble introduction to some aspects of Moduli Theory.
Classification of Algebraic Varieties
Author: Carel Faber
Publisher: European Mathematical Society
Published: 2011
Total Pages: 356
ISBN-13: 9783037190074
DOWNLOAD EBOOKFascinating and surprising developments are taking place in the classification of algebraic varieties. The work of Hacon and McKernan and many others is causing a wave of breakthroughs in the minimal model program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field. Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony to the sudden advances that originate from these new ideas. This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers.
Lectures on Invariant Theory
Author: Igor Dolgachev
Publisher: Cambridge University Press
Published: 2003-08-07
Total Pages: 244
ISBN-13: 9780521525480
DOWNLOAD EBOOKThe primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.
Quasi-projective Moduli for Polarized Manifolds
Author: Eckart Viehweg
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 329
ISBN-13: 3642797458
DOWNLOAD EBOOKThe 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.
