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Rigid Schubert varieties in compact Hermitian symmetric spaces

Publication ,  Journal Article
Robles, C; The, D
Published in: Selecta Mathematica, New Series
August 1, 2012

Given a singular Schubert variety X w in a compact Hermitian symmetric space X, it is a long-standing question to determine when X w is homologous to a smooth variety Y. We identify those Schubert varieties for which there exist first-order obstructions to the existence of Y. This extends (independent) work of M. Walters, R. Bryant and J. Hong. Key tools include (i) a new characterization of Schubert varieties that generalizes the well-known description of the smooth Schubert varieties by connected sub-diagrams of a Dynkin diagram and (ii) an algebraic Laplacian (à la Kostant), which is used to analyze the Lie algebra cohomology group associated with the problem. © 2012 Springer Basel AG.

Duke Scholars

Published In

Selecta Mathematica, New Series

DOI

EISSN

1420-9020

ISSN

1022-1824

Publication Date

August 1, 2012

Volume

18

Issue

3

Start / End Page

717 / 777

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0101 Pure Mathematics
 

Citation

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Robles, C., & The, D. (2012). Rigid Schubert varieties in compact Hermitian symmetric spaces. Selecta Mathematica, New Series, 18(3), 717–777. https://doi.org/10.1007/s00029-011-0082-y
Robles, C., and D. The. “Rigid Schubert varieties in compact Hermitian symmetric spaces.” Selecta Mathematica, New Series 18, no. 3 (August 1, 2012): 717–77. https://doi.org/10.1007/s00029-011-0082-y.
Robles C, The D. Rigid Schubert varieties in compact Hermitian symmetric spaces. Selecta Mathematica, New Series. 2012 Aug 1;18(3):717–77.
Robles, C., and D. The. “Rigid Schubert varieties in compact Hermitian symmetric spaces.” Selecta Mathematica, New Series, vol. 18, no. 3, Aug. 2012, pp. 717–77. Scopus, doi:10.1007/s00029-011-0082-y.
Robles C, The D. Rigid Schubert varieties in compact Hermitian symmetric spaces. Selecta Mathematica, New Series. 2012 Aug 1;18(3):717–777.
Journal cover image

Published In

Selecta Mathematica, New Series

DOI

EISSN

1420-9020

ISSN

1022-1824

Publication Date

August 1, 2012

Volume

18

Issue

3

Start / End Page

717 / 777

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0101 Pure Mathematics