[PDF] Symmetric Varieties Associated To Hermitian Symmetric Spaces eBook

Author : Avner Ash
Publisher : Cambridge University Press
Page : 241 pages
File Size : 44,85 MB
Release : 2010-01-14
Category : Mathematics
ISBN : 0521739551

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The new edition of this celebrated and long-unavailable book preserves the original book's content and structure and its unrivalled presentation of a universal method for the resolution of a class of singularities in algebraic geometry.

Author : Jürgen Berndt
Publisher : de Gruyter
Page : 0 pages
File Size : 23,69 MB
Release : 2022
Category : Mathematics
ISBN : 9783110689785

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Hermitian symmetric spaces are an important class of manifolds that can be studied with methods from Kähler geometry and Lie theory. This work gives an introduction to Hermitian symmetric spaces and their submanifolds, and presents classifi cation results for real hypersurfaces in these spaces, focusing on results obtained by Jürgen Berndt and Young Jin Suh in the last 20 years.

Author : Ichiro Satake
Publisher : Princeton University Press
Page : 340 pages
File Size : 40,49 MB
Release : 2014-07-14
Category : Mathematics
ISBN : 1400856809

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This book is a comprehensive treatment of the general (algebraic) theory of symmetric domains. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Robert L. Bryant
Publisher :
Page : 144 pages
File Size : 20,3 MB
Release : 2010
Category : Mathematics
ISBN : 9780691096346

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This book investigates the geometry of complex subvarieties of compact Hermitian symmetric spaces, particularly the complex Grassmannians, which are central to Schubert calculus and its applications to enumerative algebraic geometry. To do so, Robert Bryant employs a combination of Hermitian differential geometry, calibrations, and classical moving frame constructions. The main result is that, for Hermitian symmetric spaces M of rank greater than 1, there are homology classes c (called extremal) such that the complex varieties V in M that represent c display rigidity in unexpected ways. There are other cycles that display a weaker form of this sort of rigidity, but whose moduli space of representing cycles can still be described in terms of the geometry of subvarieties of related complex projective spaces. These results have applications to other problems in algebraic geometry. For example, for a holomorphic bundle E over a compact complex manifold M that is generated by its sections, the Schur polynomials in its Chern classes are known to be non-negative. The above results allow one to give a complete description of such bundles in several cases where one of these Schur polynomials actually vanishes. The book, which will interest researchers and graduate students in complex algebraic geometry or differential geometry, contains a thorough exposition of the geometry of Hermitian symmetric spaces and their Schubert cycles and characteristic classes as well as other preparatory material needed to obtain the results.

Author : Yves Guivarc'h
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 43,58 MB
Release : 1998-08-26
Category : Mathematics
ISBN : 9780817638993

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The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of the interrelationships among these various compactifications and, in particular, focuses on the martin compactifications. It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view. The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students.