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Singular Loci of Schubert Varieties Sara Sarason

Singular Loci of Schubert Varieties By Sara Sarason

Singular Loci of Schubert Varieties by Sara Sarason


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Summary

"Singular Loci of Schubert Varieties" is a unique work at the crossroads of representation theory, algebraic geometry, and combinatorics.

Singular Loci of Schubert Varieties Summary

Singular Loci of Schubert Varieties by Sara Sarason

"Singular Loci of Schubert Varieties" is a unique work at the crossroads of representation theory, algebraic geometry, and combinatorics. Over the past 20 years, many research articles have been written on the subject in notable journals. In this work, Billey and Lakshmibai have recreated and restructured the various theories and approaches of those articles and present a clearer understanding of this important subdiscipline of Schubert varieties namely singular loci. The main focus, therefore, is on the computations for the singular loci of Schubert varieties and corresponding tangent spaces. The methods used include standard monomial theory, the nil Hecke ring, and Kazhdan-Lusztig theory. New results are presented with sufficient examples to emphasize key points. A comprehensive bibliography, index, and tables the latter not to be found elsewhere in the mathematics literature round out this concise work. After a good introduction giving background material, the topics are presented in a systematic fashion to engage a wide readership of researchers and graduate students.

Singular Loci of Schubert Varieties Reviews

"The authors review the major papers in the topic that have been written during the last two decades, giving a comprehensive bibliographythis is a very important survey of the subject."

-Mathematical Reviews

Table of Contents

1. Introduction.- 2. Generalities on G/B and G/Q.- 3. Specifics for the Classical Groups.- 4. The Tangent Space and Smoothness.- 5. Root System Description of T(w, ?).- 6. Rational Smoothness and Kazhdan-Lusztig Theory.- 7. Nil-Hecke Ring and the Singular Locus of X(w).- 8. Patterns, Smoothness and Rational Smoothness.- 9. Minuscule and cominuscule G/P.- 10. Rank Two Results.- 11. Related Combinatorial Results.- 12. Related Varieties.- 13. Addendum.

Additional information

NPB9781461270942
9781461270942
1461270944
Singular Loci of Schubert Varieties by Sara Sarason
New
Paperback
Springer-Verlag New York Inc.
2012-11-07
251
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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