22 research outputs found
Automorphism groups of compact complex surfaces
We study automorphism groups and birational automorphism groups of compact complex surfaces. We show that the automorphism group of such surface is always Jordan, and the birational automorphism group is Jordan unless is birational to a product of an elliptic and a rational curve
Spitsbergen volume : Frontiers of Rationality
This volume contains 20 papers related to the workshop Frontiers of Rationality that was held in Longyearbyen, Spitsbergen, in July 2014
Exceptional del Pezzo hypersurfaces
We compute global log canonical thresholds of a large class of quasismooth
well-formed del Pezzo weighted hypersurfaces in
. As a corollary we obtain the existence
of orbifold K\"ahler--Einstein metrics on many of them, and classify
exceptional and weakly exceptional quasismooth well-formed del Pezzo weighted
hypersurfaces in .Comment: 149 pages, one reference adde
Three embeddings of the Klein simple group into the Cremona group of rank three
We study the action of the Klein simple group G consisting of 168 elements on
two rational threefolds: the three-dimensional projective space and a smooth
Fano threefold X of anticanonical degree 22 and index 1. We show that the
Cremona group of rank three has at least three non-conjugate subgroups
isomorphic to G. As a by-product, we prove that X admits a Kahler-Einstein
metric, and we construct a smooth polarized K3 surface of degree 22 with an
action of the group G.Comment: 43 page
Alpha-invariants and purely log terminal blow-ups
We prove that the sum of the α-invariants of two different Kollár components of a Kawamata log terminal singularity is less than 1. © 2018, The Author(s
The Calabi problem for smooth Fano threefolds
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