"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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"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
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2 of 3 people found the following review helpful:
5.0 out of 5 stars
Great stuff!!,
By "georgeliot" (New York, NY USA) - See all my reviews
This review is from: Singular Loci of Schubert Varieties (Progress in Mathematics) (Hardcover)
This is by far the best book on Schubert varieties that I have ever seen. Precise, yet detailed, thorough but never pedantic. Billey is a wonder. The writing, though admirably confined to math, is poetic; never more so, than in that lyrical sentence that begins "Let there be a Wyle space..."
5.0 out of 5 stars
Illuminates the subject matter,
This review is from: Singular Loci of Schubert Varieties (Progress in Mathematics) (Hardcover)
Clear, cogent, and to the point. Explores the relevant variables and delivers the goods. A must read for Schubert afficionados.
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Inside This Book
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First Sentence:
The study of Schubert varieties arising out of 19th century classical projective geometry took on a more modern treatment with the work of Ehresmann, then Chevalley, and later Bernstein, Gelfand, Gelfand and Demazure. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rational smoothness, extremal weight vectors, ladder determinantal varieties, opposite big cell, bert varieties, minuscule fundamental weights, quiver varieties, maximal parabolic subgroup, signed notation, standard monomial theory, singular loci, singular locus, affine neighborhood, unipotent part, monomial order, smoothness criteria, minimal representatives, opposite cell, row indices, small resolution, rational singularities, bad pattern, admissible pair, maximal torus, unipotent subgroup Key Phrases - Capitalized Phrases (CAPs): (learn more)
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The study of Schubert varieties arising out of 19th century classical projective geometry took on a more modern treatment with the work of Ehresmann, then Chevalley, and later Bernstein, Gelfand, Gelfand and Demazure. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rational smoothness, extremal weight vectors, ladder determinantal varieties, opposite big cell, bert varieties, minuscule fundamental weights, quiver varieties, maximal parabolic subgroup, signed notation, standard monomial theory, singular loci, singular locus, affine neighborhood, unipotent part, monomial order, smoothness criteria, minimal representatives, opposite cell, row indices, small resolution, rational singularities, bad pattern, admissible pair, maximal torus, unipotent subgroup Key Phrases - Capitalized Phrases (CAPs): (learn more)
Using Laplace New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 10
books:
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19
books
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- Representations of Algebraic Groups (Mathematical Surveys and Monographs) by Jens Carsten Jantzen on page 7, and Back Matter
- Linear Algebraic Groups (Graduate Texts in Mathematics) by Armand Borel on page 7, and Back Matter
- Geometry of Coxeter Groups (Chapman & Hall/CRC Research Notes in Mathematics Series) by Howard Hiller in Back Matter
- An Introduction to Intersection Homology Theory, Second Edition by Frances Kirwan in Back Matter
- Algebraic Geometry: A First Course (Graduate Texts in Mathematics) (v. 133) by Joe Harris in Back Matter
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- Frobenius Splitting Methods in Geometry and Representation Theory (Progress in Mathematics) by Michel Brion in Back Matter (1), and Back Matter (2)
- Complex Tori (Progress in Mathematics) by Herbert Lange in Back Matter
- Lie Groups: Beyond an Introduction by Anthony W. Knapp in Back Matter
- A Tribute to C.S. Seshadri: A Collection of Articles on Geometry and Representation Theory (Trends in Mathematics) by Venkatrama Lakshmibai in Back Matter
- Geometric Analysis and Applications to Quantum Field Theory (Progress in Mathematics) by Peter Bouwknegt in Back Matter
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