Salem polynomials and the bimeromorphic automorphism group of a hyper-Kähler manifold

2010 ◽  
pp. 201-227 ◽  
Author(s):  
Keiji Oguiso
Keyword(s):  
Automorphism Group ◽  
Kähler Manifold ◽  
Kahler Manifold

scholarly journals NO COHOMOLOGICALLY TRIVIAL NONTRIVIAL AUTOMORPHISM OF GENERALIZED KUMMER MANIFOLDS

2018 ◽  
Vol 239 ◽  
pp. 110-122
Author(s):  
KEIJI OGUISO
Keyword(s):  
Automorphism Group ◽  
Recent Work ◽  
Cohomology Group ◽  
Kähler Manifold ◽  
Nontrivial Automorphism ◽  
Kahler Manifold

For a hyper-Kähler manifold deformation equivalent to a generalized Kummer manifold, we prove that the action of the automorphism group on the total Betti cohomology group is faithful. This is a sort of generalization of a work of Beauville and a more recent work of Boissière, Nieper-Wisskirchen, and Sarti, concerning the action of the automorphism group of a generalized Kummer manifold on the second cohomology group.

scholarly journals Geometry and Automorphisms of Non-Kähler Holomorphic Symplectic Manifolds

2021 ◽  
Author(s):  
Fedor Bogomolov ◽  
Nikon Kurnosov ◽  
Alexandra Kuznetsova ◽  
Egor Yasinsky
Keyword(s):  
Automorphism Group ◽  
Projective Space ◽  
Kähler Manifold ◽  
Symplectic Manifolds ◽  
Finite Degree ◽  
Partial Classification ◽  
Kahler Manifold ◽  
Degeneracy Locus ◽  
Algebraic Reduction

Abstract We consider the only one known class of non-Kähler irreducible holomorphic symplectic manifolds, described in the works by D. Guan and the 1st author. Any such manifold $Q$ of dimension $2n-2$ is obtained as a finite degree $n^2$ cover of some non-Kähler manifold $W_F$, which we call the base of $Q$. We show that the algebraic reduction of $Q$ and its base is the projective space of dimension $n-1$. Besides, we give a partial classification of submanifolds in $Q$, describe the degeneracy locus of its algebraic reduction and prove that the automorphism group of $Q$ satisfies the Jordan property.

scholarly journals Relative non-pluripolar product of currents

2021 ◽  
Author(s):  
Duc-Viet Vu
Keyword(s):  
Kähler Manifold ◽  
Monotonicity Property ◽  
Necessary Condition ◽  
Positive Current ◽  
Lelong Numbers ◽  
Kahler Manifold ◽  
Closed Positive Current ◽  
Positive Currents ◽  
Compact Kähler Manifold

AbstractLet X be a compact Kähler manifold. Let $$T_1, \ldots , T_m$$ T 1 , … , T m be closed positive currents of bi-degree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the non-pluripolar product relative to T of $$T_1, \ldots , T_m$$ T 1 , … , T m . We recover the well-known non-pluripolar product of $$T_1, \ldots , T_m$$ T 1 , … , T m when T is the current of integration along X. Our main results are a monotonicity property of relative non-pluripolar products, a necessary condition for currents to be of relative full mass intersection in terms of Lelong numbers, and the convexity of weighted classes of currents of relative full mass intersection. The former two results are new even when T is the current of integration along X.

A POSITIVITY PROPERTY FOR FOLIATIONS ON COMPACT KÄHLER MANIFOLDS

2006 ◽  
Vol 17 (01) ◽  
pp. 35-43 ◽  
Author(s):  
MARCO BRUNELLA
Keyword(s):  
Kähler Manifold ◽  
Rational Curves ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Canonical Bundle ◽  
Positivity Property ◽  
Kahler Manifold ◽  
Compact Kähler Manifold

We prove that the canonical bundle of a foliation by curves on a compact Kähler manifold is pseudoeffective, unless the foliation is a (special) foliation by rational curves.

Frölicher–Nijenhuis cohomology on G2- and Spin(7)-manifolds

2018 ◽  
Vol 29 (12) ◽  
pp. 1850075
Author(s):  
Kotaro Kawai ◽  
Hông Vân Lê ◽  
Lorenz Schwachhöfer
Keyword(s):  
Riemannian Manifold ◽  
Differential Form ◽  
Kähler Manifold ◽  
Cohomology Groups ◽  
Kahler Manifold ◽  
Partial Description ◽  
Nijenhuis Bracket

In this paper, we show that a parallel differential form [Formula: see text] of even degree on a Riemannian manifold allows to define a natural differential both on [Formula: see text] and [Formula: see text], defined via the Frölicher–Nijenhuis bracket. For instance, on a Kähler manifold, these operators are the complex differential and the Dolbeault differential, respectively. We investigate this construction when taking the differential with respect to the canonical parallel [Formula: see text]-form on a [Formula: see text]- and [Formula: see text]-manifold, respectively. We calculate the cohomology groups of [Formula: see text] and give a partial description of the cohomology of [Formula: see text].

scholarly journals On some compact almost Kähler locally symmetric space

1998 ◽  
Vol 21 (1) ◽  
pp. 69-72 ◽  
Author(s):  
Takashi Oguro
Keyword(s):  
Symmetric Space ◽  
Scalar Curvature ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Locally Symmetric Space ◽  
Kahler Manifold ◽  
Almost Kähler

In the framework of studying the integrability of almost Kähler manifolds, we prove that if a compact almost Kähler locally symmetric spaceMis a weakly ,∗-Einstein vnanifold with non-negative ,∗-scalar curvature, thenMis a Kähler manifold.

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