scholarly journals Fano manifolds of index n − 2 and the cone conjecture

2017 ◽  
Vol 166 (1) ◽  
pp. 1-31
Author(s):  
IZZET COSKUN ◽  
ARTIE PRENDERGAST-SMITH
Keyword(s):  
Automorphism Group ◽  
Fano Manifolds ◽  
Fundamental Domains ◽  
Nef Cone

AbstractThe Morrison–Kawamata Cone Conjecture predicts that the action of the automorphism group on the effective nef cone and the action of the pseudo-automorphism group on the effective movable cone of a klt Calabi–Yau pair have rational, polyhedral fundamental domains. In [CPS], we proved the conjecture for certain blowups of Fano manifolds of index n - 1. In this paper, we consider the Morrison–Kawamata conjecture for blowups of Fano manifolds of index n - 2.

scholarly journals Ricci Iteration for Coupled Kähler–Einstein Metrics

2019 ◽  
Author(s):  
Ryosuke Takahashi
Keyword(s):  
Dynamical System ◽  
Automorphism Group ◽  
Chern Class ◽  
Einstein Metrics ◽  
Fano Manifolds ◽  
Ricci Operator ◽  
Smooth Convergence ◽  
Kähler Einstein Metrics

Abstract In this paper, we introduce the “coupled Ricci iteration”, a dynamical system related to the Ricci operator and twisted Kähler–Einstein metrics as an approach to the study of coupled Kähler–Einstein (CKE) metrics. For negative 1st Chern class, we prove the smooth convergence of the iteration. For positive 1st Chern class, we also provide a notion of coercivity of the Ding functional and show its equivalence to the existence of CKE metrics. As an application, we prove the smooth convergence of the iteration on CKE Fano manifolds assuming that the automorphism group is discrete.

scholarly journals K-STABILITY OF FANO MANIFOLDS WITH NOT SMALL ALPHA INVARIANTS

2017 ◽  
Vol 18 (3) ◽  
pp. 519-530 ◽  
Author(s):  
Kento Fujita
Keyword(s):  
Automorphism Group ◽  
Einstein Metrics ◽  
Holomorphic Automorphism ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Kähler Einstein Metrics ◽  
Holomorphic Automorphism Group

We show that any $n$-dimensional Fano manifold $X$ with $\unicode[STIX]{x1D6FC}(X)=n/(n+1)$ and $n\geqslant 2$ is K-stable, where $\unicode[STIX]{x1D6FC}(X)$ is the alpha invariant of $X$ introduced by Tian. In particular, any such $X$ admits Kähler–Einstein metrics and the holomorphic automorphism group $\operatorname{Aut}(X)$ of $X$ is finite.

scholarly journals On the automorphism group of a symplectic half-flat 6-manifold

2019 ◽  
Vol 31 (1) ◽  
pp. 265-273
Author(s):  
Fabio Podestà ◽  
Alberto Raffero
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Group Action ◽  
Cohomogeneity One ◽  
Cohomogeneity One Action

Abstract We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat {\mathrm{SU}(3)} -structure has Abelian Lie algebra with dimension bounded by {\min\{5,b_{1}(M)\}} . Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on {T\mathbb{S}^{3}} which are invariant under a cohomogeneity one action of {\mathrm{SO}(4)} .

scholarly journals ON EDGE-PRIMITIVE GRAPHS WITH SOLUBLE EDGE-STABILIZERS

2021 ◽  
pp. 1-28
Author(s):  
HUA HAN ◽  
HONG CI LIAO ◽  
ZAI PING LU
Keyword(s):  
Automorphism Group

Abstract A graph is edge-primitive if its automorphism group acts primitively on the edge set, and $2$ -arc-transitive if its automorphism group acts transitively on the set of $2$ -arcs. In this paper, we present a classification for those edge-primitive graphs that are $2$ -arc-transitive and have soluble edge-stabilizers.

scholarly journals Affine cones over cubic surfaces are flexible in codimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Perepechko
Keyword(s):  
Automorphism Group ◽  
Open Subset ◽  
Pezzo Surface ◽  
Ample Divisor ◽  
Transitive Action ◽  
Del Pezzo Surface ◽  
Codimension One ◽  
Cubic Surfaces ◽  
Special Automorphism ◽  
Del Pezzo

AbstractLet Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

Automorphism group and representation of a twisted multi-loop algebra

2010 ◽  
Vol 26 (1) ◽  
pp. 143-154 ◽  
Author(s):  
Cui Chen ◽  
Hai Feng Lian ◽  
Shao Bin Tan
Keyword(s):  
Automorphism Group ◽  
Loop Algebra
Sign in / Sign up

Export Citation Format

Share Document