<p>"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." </p>
<p>-Mathematical Reviews</p>

"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.

Les mer

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

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.
Les mer
Springer Book Archives
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer

Produktdetaljer

ISBN
9780817640927
Publisert
2000-09-29
Utgiver
Birkhauser Boston Inc
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, UU, UP, P, 05, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
251