Rigidity and Quasi-Rigidity of External Cycles in Hermitian Sytems 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Bryant, Robert L. 作者

Princeton Univ Pr

译者

2010-2 出版日期

144 页数

$ 55.94 价格

HRD

丛书系列

9780691096292 图书编码

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Rigidity and Quasi-Rigidity of External Cycles in Hermitian Sytems 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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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.

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