# ePub Rigidity and Quasi-Rigidity of Extremal Cycles in Hermitian Symmetric Spaces. (AM-153), Volume 153 (Annals of Mathematics Studies) download

# by Robert L. Bryant

Am-153), Volume 153 as Want to Read . The 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.

Am-153), Volume 153 as Want to Read: Want to Read savin. ant to Read. To do so, Robert Bryant employs a combination of Hermitian differential geometry, calibrations, and classical moving frame constructions.

Out of Stock To do so, Robert Bryant employs a combination of Hermitian differential .

Rigidity and Quasi-Rigidity of Extremal Cycles in Hermitian Symmetric Spaces. Get a quote for your Rigidity and Quasi-Rigidity of Extremal Cycles in Hermitian Symmetric Spaces. 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.

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Rigidity and Quasi-Rigidity of Extremal Cycles in Hermitian Symmetric.

How is Chegg Study better than a printed Rigidity and Quasi-Rigidity of. .

How is Chegg Study better than a printed Rigidity and Quasi-Rigidity of Extremal Cycles in Hermitian Symmetric Spaces (AM-153) student solution manual from the bookstore? Our interactive player makes it easy to find solutions to Rigidity and Quasi-Rigidity of Extremal Cycles in Hermitian Symmetric Spaces (AM-153) problems you're working on - just go to the chapter for your book.

Mathematics Differential Geometry Abstract: I use local differential geometric techniques to prove that the algebraic cycles in certain extremal.

Mathematics Differential Geometry. Title:Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces. Authors:Robert L. Bryant. Submitted on 24 Jun 2000 (v1), last revised 5 Mar 2001 (this version, v2)). Abstract: I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (. deformable only by ambient motions) or quasi-rigid (roughly speaking, foliated by rigid subvarieties in a nontrivial way).

I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (. These rigidity results have a number of applications: First, they prove that many subvarieties in Grassmannians and other Hermitian symmetric spaces cannot be smoothed (. are not homologous to a smooth subvariety).

Rigidity and Quasi-Rigidity of Extremal Cycles in Hermitian Symmetric Spaces, Annals of Mathematics Studies, vol. 153. Princeton University Press, Princeton. arXiv:math/0006186 (2010)Google Scholar. 6. Čap, . Slovák, . Parabolic Geometries.

It follows from the Mostow rigidity theorem that the group of isometries of a finite-volume hyperbolic n-manifold . Mostow, G. D. (1973), Strong rigidity of locally symmetric spaces, Annals of mathematics studies, 78, Princeton University Press, ISBN 978-0-691-08136-6, MR 0385004.

It follows from the Mostow rigidity theorem that the group of isometries of a finite-volume hyperbolic n-manifold M (for n 2) is finite and isomorphic to. Out ( π 1 ( M ) ) {displaystyle operatorname {Out} (pi {1}(M))}. Prasad, Gopal (1973), "Strong rigidity of Q-rank 1 lattices", Inventiones Mathematicae, 21: 255–286, doi:10. 1007/BF01418789, ISSN 002910, MR 0385005.

Article in American Journal of Mathematics 124(6) . Similar lower bounds are also obtained in the case of Hermitian symmetric spaces of noncompact type.

Article in American Journal of Mathematics 124(6):1221-1246 · December 2002 with 12 Reads. How we measure 'reads'. In his seminal work Calabi established the foundation on the study of holomorphic isometries from a Kähler manifold with real analytic local potential functions into complex space forms, . Fubini-Study spaces. This leads to interior extension results on germs of holomorphic isometries between bounded domains.

Find nearly any book by Robert L. Get the best deal by comparing prices from over 100,000 booksellers. AM-153), Volume 153 (Annals of Mathematics Studies): Rigidity and Quasi-Rigidity of Extremal Cycles in Hermitian Symmetric Spaces. AM-153), Volume 153 (Annals of Mathematics Studies): ISBN 9780691096346 (978-0-691-09634-6) Softcover, Princeton University Press, 2002. Rigidity and Quasi-Rigidity of Extremal Cycles in Hermitian Symmetric Spaces.

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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