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Full Description
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.
Contents
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.
