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Toric Varieties


About this Title

David A. Cox, Amherst College, MA, John B. Little, College of the Holy Cross, Worcester, MA and Henry K. Schenck, University of Illinois at Urbana-Champaign, Urbana, IL

Publication: Graduate Studies in Mathematics
Publication Year 2011: Volume 124
ISBNs: 978-0-8218-4819-7 (print); 978-1-4704-1185-5 (online)
DOI: http://dx.doi.org/10.1090/gsm/124
MathSciNet review: MR2810322
MSC: Primary 14M25; Secondary 05A15, 05E45, 52B12

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Table of Contents


Part I. Basic theory of toric varieties

  • Chapter 1. Affine toric varieties
  • Chapter 2. Projective toric varieties
  • Chapter 3. Normal toric varieties
  • Chapter 4. Divisors on toric varieties
  • Chapter 5. Homogeneous coordinates on toric varieties
  • Chapter 6. Line bundles on toric varieties
  • Chapter 7. Projective toric morphisms
  • Chapter 8. The canonical divisor of a toric variety
  • Chapter 9. Sheaf cohomology of toric varieties

Topics in toric geometry

  • Chapter 10. Toric surfaces
  • Chapter 11. Toric resolutions and toric singularities
  • Chapter 12. The topology of toric varieties
  • Chapter 13. Toric Hirzebruch-Riemann-Roch
  • Chapter 14. Toric GIT and the secondary fan
  • Chapter 15. Geometry of the secondary fan
  • Appendix A. The history of toric varieties
  • Appendix B. Computational methods
  • Appendix C. Spectral sequences