Birational geometry of algebraic varieties. (English) Zbl 1441.14053
Sirakov, Boyan (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2018, Rio de Janeiro, Brazil, August 1–9, 2018. Volume II. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 565-590 (2018).
Summary: This is a report on some of the main developments in birational geometry in recent years focusing on the minimal model program, Fano varieties, singularities and related topics, in characteristic zero.
For the entire collection see [Zbl 1437.00044].
For the entire collection see [Zbl 1437.00044].
MSC:
| 14E30 | Minimal model program (Mori theory, extremal rays) |
| 14J45 | Fano varieties |
| 14B05 | Singularities in algebraic geometry |
| 14C20 | Divisors, linear systems, invertible sheaves |
| 14E05 | Rational and birational maps |
| 14E07 | Birational automorphisms, Cremona group and generalizations |
| 14-02 | Research exposition (monographs, survey articles) pertaining to algebraic geometry |
| 14-03 | History of algebraic geometry |
| 01A61 | History of mathematics in the 21st century |
