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Singular Loci of Schubert Varieties: Progress in Mathematics, cartea 182

Autor Sara Sarason, V. Lakshmibai
en Limba Engleză Hardback – 29 sep 2000
"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.
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Specificații

ISBN-13: 9780817640927
ISBN-10: 0817640924
Pagini: 251
Ilustrații: XII, 251 p.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.55 kg
Ediția:2000
Editura: Birkhäuser Boston
Colecția Birkhäuser
Seria Progress in Mathematics

Locul publicării:Boston, MA, United States

Public țintă

Research

Cuprins

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.

Recenzii

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