K-stability of Fano varieties: an algebro-geometric approach
C Xu - EMS Surveys in Mathematical Sciences, 2021 - content.ems.press
K-stability of Fano varieties: an algebro-geometric approach Page 1 EMS Surv. Math. Sci. 8 (2021),
265–354 DOI 10.4171/EMSS/51 © 2021 European Mathematical Society Published by EMS …
265–354 DOI 10.4171/EMSS/51 © 2021 European Mathematical Society Published by EMS …
The volume of singular Kähler–Einstein Fano varieties
Y Liu - Compositio Mathematica, 2018 - cambridge.org
We show that the anti-canonical volume of an for ideals and the normalized volume function
for real valuations. This refines a recent result by Fujita. As an application, we get sharp …
for real valuations. This refines a recent result by Fujita. As an application, we get sharp …
Seshadri constants for vector bundles
M Fulger, T Murayama - Journal of Pure and Applied Algebra, 2021 - Elsevier
We introduce Seshadri constants for line bundles in a relative setting. They generalize the
classical Seshadri constants of line bundles on projective varieties and their extension to …
classical Seshadri constants of line bundles on projective varieties and their extension to …
On the sharpness of Tian's criterion for K-stability
Tian's criterion for K-stability states that a Fano variety of dimension n whose alpha invariant
is greater than is K-stable. We show that this criterion is sharp by constructing n-dimensional …
is greater than is K-stable. We show that this criterion is sharp by constructing n-dimensional …
On K-stability, height bounds and the Manin-Peyre conjecture
RJ Berman - arxiv preprint arxiv:2305.07272, 2023 - arxiv.org
This note discusses some intriguing connections between height bounds on complex K-
semistable Fano varieties X and Peyre's conjectural formula for the density of rational points …
semistable Fano varieties X and Peyre's conjectural formula for the density of rational points …
Sharp bounds on the height of K-semistable toric Fano varieties, I
Inspired by Fujita's algebro-geometric result that complex projective space has maximal
degree among all K-semistable Fano varieties, we conjecture that the height of a K …
degree among all K-semistable Fano varieties, we conjecture that the height of a K …
Fano foliations with small algebraic ranks
J Liu - Advances in Mathematics, 2023 - Elsevier
In this paper we study the algebraic ranks of foliations on Q-factorial normal projective
varieties. We start by establishing a Kobayashi-Ochiai's theorem for Fano foliations in terms …
varieties. We start by establishing a Kobayashi-Ochiai's theorem for Fano foliations in terms …
Frobenius-Seshadri constants and characterizations of projective space
T Murayama - arxiv preprint arxiv:1701.00511, 2017 - arxiv.org
We introduce higher-order variants of the Frobenius-Seshadri constant due to Musta\c {t}\u
{a} and Schwede, which are defined for ample line bundles in positive characteristic. These …
{a} and Schwede, which are defined for ample line bundles in positive characteristic. These …
[HTML][HTML] Fano varieties with large Seshadri constants
Z Zhuang - Advances in Mathematics, 2018 - Elsevier
We show that the set of Fano varieties (with arbitrary singularities) whose anticanonical
divisors have large Seshadri constants satisfies certain weak and birational boundedness …
divisors have large Seshadri constants satisfies certain weak and birational boundedness …
Seshadri constants of equivariant vector bundles on toric varieties
We compute Seshadri constants of a torus equivariant nef vector bundle on a projective
space satisfying certain conditions. As an application, we compute Seshadri constants of …
space satisfying certain conditions. As an application, we compute Seshadri constants of …