The Calabi problem for smooth Fano threefolds

Abstract

To be published by CUP, LMS Lecture Notes Series 2022Copyright © 2021 The Authors. There are 105 irreducible families of smooth Fano threefolds, which have been classified by Iskovskikh, Mori and Mukai. For each family, we determine whether its general member admits a K¨ahler–Einstein metric or not. We also find all K¨ahler–Einstein smooth Fano threefolds that have infinite automorphism groups.Engineering & Physical Sciences Research Council (EP/056689/1 Calabi conjecture for smooth Fano threefolds); Heilbronn Institute for Mathematical Research (K-stability of smooth Fano 3-folds).https://archive.mpim-bonn.mpg.de/id/eprint/4589/1/mpim-preprint_2021-31.pd