Klaus Hulek - Böcker

This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory.The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.

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This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry

The Bayreuth meeting on "Complex Algebraic Varieties"focussed on the classification of algebraic varieties andtopics such as vector bundles, Hodge theory and hermitiandifferential geometry. Most of the articles in this volumeare closely related to talks given at the conference: allare original, fully refereed research articles.CONTENTS: A. Beauville: Annulation du H(1) pour les fibresen droites plats.- M. Beltrametti, A.J. Sommese, J.A.Wisniewski: Results on varieties with many lines and theirapplications to adjunction theory.- G. Bohnhorst, H.Spindler: The stability of certain vector bundles on P(n) .-F. Catanese, F. Tovena: Vector bundles, linear systems andextensions of (1).- O. Debarre: Vers uns stratification del'espace des modules des varietes abeliennes principalementpolarisees.- J.P. Demailly: Singular hermitian metrics onpositive line bundles.- T. Fujita: On adjoint bundles ofample vector bundles.- Y. Kawamata: Moderate degenerationsof algebraic surfaces.- U. Persson: Genus two fibrationsrevisited.- Th. Peternell, M. Szurek, J.A. Wisniewski:Numerically effective vector bundles with small Chernclasses.- C.A.M. Peters: On the rank of non-rigid periodmaps in the weight one and two case.- A.N. Tyurin: Thegeometry of the special components of moduli space of vectorbundles over algebraic surfaces of general type.

This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry

This volume contains the Proceedings of the conference "Complex and Differential Geometry 2009", held at Leibniz Universität Hannover, September 14 - 18, 2009. It was the aim of this conference to bring specialists from differential geometry and (complex) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in (classical) algebraic geometry through complex geometry, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology.

Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in (classical) algebraic geometry through complex geometry, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology.