scholarly journals Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kähler deformation

2005 ◽  
Vol 160 (3) ◽  
pp. 591-645 ◽  
Author(s):  
Jun-Muk Hwang ◽  
Ngaiming Mok
Keyword(s):  
Homogeneous Spaces ◽  
Picard Number ◽  
Projective Varieties

scholarly journals On the classification of 3-dimensionalSL2(ℂ)-varieties

2000 ◽  
Vol 157 ◽  
pp. 129-147 ◽  
Author(s):  
Stefan Kebekus
Keyword(s):  
Automorphism Group ◽  
Semisimple Group ◽  
Picard Number ◽  
Projective Varieties ◽  
3 Dimensional

In the present work we describe 3-dimensional complexSL2-varieties where the genericSL2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group acts such that the generic orbits are 2-dimensional.This is an ingredient of the classification [Keb99] of the 3-dimensional relatively minimal quasihomogeneous varieties where the automorphism group is not solvable.

scholarly journals Kähler–Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 102
Author(s):  
Jae-Hyouk Lee ◽  
Kyeong-Dong Park ◽  
Sungmin Yoo
Keyword(s):  
Einstein Metrics ◽  
Homogeneous Spaces ◽  
Picard Number ◽  
Spherical Varieties ◽  
Symmetric Varieties ◽  
Moment Polytope ◽  
Kähler Einstein Metrics ◽  
Moment Polytopes

Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit Kähler–Einstein metrics by using a combinatorial criterion for K-stability of Fano spherical varieties obtained by Delcroix. For this purpose, we present their algebraic moment polytopes and compute the barycenter of each moment polytope with respect to the Duistermaat–Heckman measure.

scholarly journals A note on Kawaguchi–Silverman conjecture

2021 ◽  
Vol 32 (11) ◽  
Author(s):  
Sichen Li ◽  
Yohsuke Matsuzawa
Keyword(s):  
Automorphism Groups ◽  
Fano Variety ◽  
Picard Number ◽  
Projective Varieties ◽  
Projective Bundles ◽  
Base Loci

We collect some results on endomorphisms on projective varieties related to the Kawaguchi–Silverman conjecture. We discuss certain conditions on automorphism groups of projective varieties and positivity conditions on leading real eigendivisors of self-morphisms. We prove Kawaguchi–Silverman conjecture for endomorphisms on projective bundles on a smooth Fano variety of Picard number one. In the last section, we discuss endomorphisms and augmented base loci of their eigendivisors.

Cohomological Conditions on Endomorphisms of Projective Varieties

2017 ◽  
Vol 145 (3) ◽  
pp. 449-468 ◽  
Author(s):  
Holly Krieger ◽  
Paul Reschke
Keyword(s):  
Projective Varieties
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