Higher Dimensional Algebraic Geometry
A Volume in Honor of V. V. Shokurov

A collection of research and survey papers, written by leading experts, on a variety of topics in modern algebraic geometry.

Christopher Hacon (Edited by), Chenyang Xu (Edited by)

9781009396240, Cambridge University Press

Paperback / softback, published 2 January 2025

450 pages
22.8 x 15.2 x 2.4 cm, 0.67 kg

Arising from the 2022 Japan-US Mathematics Institute, this book covers a range of topics in modern algebraic geometry, including birational geometry, classification of varieties in positive and zero characteristic, K-stability, Fano varieties, foliations, the minimal model program and mathematical physics. The volume includes survey articles providing an accessible introduction to current areas of interest for younger researchers. Research papers, written by leading experts in the field, disseminate recent breakthroughs in areas related to the research of V.V. Shokurov, who has been a source of inspiration for birational geometry over the last forty years.

1. Foreword
2. Birational geometry of algebraic varieties and Shokurov's work
3. ACC for log canonical thresholds for complex analytic spaces
4. Conjectures on the Kodaira dimension
5. Characterizing terminal Fano three folds with the smallest anti-canonical volume
6. Uniform rational polytopes for Iitaka dimensions
7. MMP for algebraically integrable foliations
8. On Toric Fano fibrations
9. Q-Fano three folds of Fano index thirteen
10. Reflective 2-elementary lattices
11. The relative duBois complex-on a question of s. Zucker
12. Factorization presentations
13. Spectrum bounds in geometry
14. On the DCC of Iitaka volumes
15. Shokurov's index conjecture for quotient singularities
16. A note on the Sarkisov program
17. Cluster varieties and Toric specializations of Fano varieties
18. Birational rigidity and alpha invariants of Fano varieties
19. On f-pure inversion of adjunction
20. On termination and fundamental groups
21. Motivic integration on Berkovich spaces.

Subject Areas: Geometry [PBM]