Non-integrated defect relation for meromorphic maps from Kähler manifolds with hypersurfaces of a projective variety in subgeneral position

2021 ◽  
Vol 73 (2) ◽  
Author(s):  
Si Duc Quang ◽  
Le Ngoc Quynh ◽  
Nguyen Thi Nhung
Keyword(s):  
Projective Variety ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Defect Relation ◽  
Meromorphic Maps

scholarly journals Canonical Heights on Hyper-Kähler Varieties and the Kawaguchi–Silverman Conjecture

2019 ◽  
Author(s):  
John Lesieutre ◽  
Matthew Satriano
Keyword(s):  
Projective Variety ◽  
Kähler Manifold ◽  
Height Function ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Dense Orbit ◽  
Canonical Height ◽  
Projective Threefolds ◽  
Higher Dimensional ◽  
Dynamical Degrees

Abstract The Kawaguchi–Silverman conjecture predicts that if $f: X \dashrightarrow X$ is a dominant rational-self map of a projective variety over $\overline{{\mathbb{Q}}}$, and $P$ is a $\overline{{\mathbb{Q}}}$-point of $X$ with a Zariski dense orbit, then the dynamical and arithmetic degrees of $f$ coincide: $\lambda _1(f) = \alpha _f(P)$. We prove this conjecture in several higher-dimensional settings, including all endomorphisms of non-uniruled smooth projective threefolds with degree larger than $1$, and all endomorphisms of hyper-Kähler manifolds in any dimension. In the latter case, we construct a canonical height function associated with any automorphism $f: X \to X$ of a hyper-Kähler manifold defined over $\overline{{\mathbb{Q}}}$. We additionally obtain results on the periodic subvarieties of automorphisms for which the dynamical degrees are as large as possible subject to log concavity.

Non-integrated defect of meromorphic maps on Kähler manifolds

2018 ◽  
Vol 292 (1-2) ◽  
pp. 211-229 ◽  
Author(s):  
Do Duc Thai ◽  
Si Duc Quang
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Meromorphic Maps

Sunada transplantation and isogeny of intermediate Jacobians of compact Kähler manifolds

2020 ◽  
Vol 72 (1) ◽  
pp. 127-147
Author(s):  
Carolyn Gordon ◽  
Eran Makover ◽  
Bjoern Muetzel ◽  
David Webb
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds
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