[see attached for complete text] {\it 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, the authors 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. Key features of this work include:

Zusammenfassung

"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

Inhalt

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.