97 research outputs found
Del Pezzo surfaces and local inequalities
I prove new local inequality for divisors on smooth surfaces, describe its
applications, and compare it to a similar local inequality that is already
known by experts.Comment: 13 pages; to appear in the proceedings of the conference "Groups of
Automorphisms in Birational and Affine Geometry", Levico Terme (Trento), 201
On A Conjecture of Tian
We study Tian's -invariant in comparison with the
-invariant for pairs consisting of a smooth surface
of degree in the projective three-dimensional space and a hyperplane
section . A conjecture of Tian asserts that .
We show that this is indeed true for (the result is well known for
), and we show that for
provided that is general enough. We also construct
examples of , for and , for which Tian's conjecture fails. We
provide a candidate counterexample for .Comment: Final version. To appear in Mathematische Zeitschrif
Log canonical thresholds of Del Pezzo Surfaces in characteristic p
The global log canonical threshold of each non-singular complex del Pezzo
surface was computed by Cheltsov. The proof used Koll\'ar-Shokurov's
connectedness principle and other results relying on vanishing theorems of
Kodaira type, not known to be true in finite characteristic.
We compute the global log canonical threshold of non-singular del Pezzo
surfaces over an algebraically closed field. We give algebraic proofs of
results previously known only in characteristic . Instead of using of the
connectedness principle we introduce a new technique based on a classification
of curves of low degree. As an application we conclude that non-singular del
Pezzo surfaces in finite characteristic of degree lower or equal than are
K-semistable.Comment: 21 pages. Thorough rewrite following referee's suggestions. To be
published in Manuscripta Mathematic
Del Pezzo surfaces with many symmetries
We classify smooth del Pezzo surfaces whose alpha-invariant of Tian is bigger
than one.Comment: 23 page
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
Alpha-invariants and purely log terminal blow-ups
We prove that the sum of the -invariants of two different Koll\'ar
components of a Kawamata log terminal singularity is less than .Comment: 12 page
Non-factorial nodal complete intersection threefolds
We give a bound on the minimal number of singularities of a nodal projective
complete intersection threefold which contains a smooth complete intersection
surface that is not a Cartier divisor
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
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
- …