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Intended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics. With numerous exercises and examples, it covers the core notions and applications of equivariant cohomology.
List of contents
1. Preview; 2. Defining equivariant cohomology; 3. Basic properties; 4. Grassmannians and flag varieties; 5. Localization I; 6. Conics; 7. Localization II; 8. Toric varieties; 9. Schubert calculus on Grassmannians; 10. Flag varieties and Schubert polynomials; 11. Degeneracy loci; 12. Infinite-dimensional flag varieties; 13. Symplectic flag varieties; 14. Symplectic Schubert polynomials; 15. Homogeneous varieties; 16. The algebra of divided difference operators; 17. Equivariant homology; 18. Bott-_Samelson varieties and Schubert varieties; 19. Structure constants; A. Algebraic topology; B. Specialization in equivariant Borel-_Moore homology; C. Pfaffians and Q-polynomials; D. Conventions for Schubert varieties; E. Characteristic classes and equivariant cohomology; References; Notation index; Subject index.
About the author
David Anderson is Associate Professor at The Ohio State University. He works in combinatorial algebraic geometry and has written over three dozen papers on topics including Schubert calculus, Newton–Okounkov bodies, and equivariant K-theory. In 2020, he received a CAREER Award from the National Science Foundation.William Fulton is Oscar Zariski Distinguished University Professor Emeritus at the University of Michigan. He is an algebraic geometer, and author or co-author of approximately five dozen papers and a dozen books, including 'Intersection Theory,' which won a Steele Prize from the American Mathematical Society. Fulton is a member of the National Academy of Sciences, and a foreign member of the Royal Swedish Academy of Sciences.
