Higher Dimensional Algebraic Geometry

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.

Christopher Hacon is the McMinn Presidential Endowed Chair and Distinguished Professor at the University of Utah. He is a Fellow of the Royal Society, a member of the National Academy of Sciences and of the American Academy of Arts and Sciences. His research in algebraic geometry has been recognized by the Clay Research Prize 2007, the Cole Prize 2009, the Feltrinelli Prize 2011, and the Breakthrough Prize in Mathematics 2018.

Chenyang Xu is Professor at Princeton University. He is a fellow of the American Mathematical Society. His contributions to algebraic geometry have been recognized by the Future Science Prize 2017, the New Horizon Prize 2019, and the Cole Prize 2021.