Adjoint linear series on weakly 1-complete Kähler manifolds II: Lefschetz type theorem on quasi-Abelian varieties

1998 ◽  
Vol 312 (2) ◽  
pp. 363-385 ◽  
Author(s):  
Shigeharu Takayama
Keyword(s):  
Abelian Varieties ◽  
Type Theorem ◽  
Linear Series ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Lefschetz Type

On the Chow ring of K3 surfaces and hyper-Kahler manifolds

2017 ◽  
Author(s):  
Claire Voisin
Keyword(s):  
Projective Space ◽  
Abelian Varieties ◽  
K3 Surfaces ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Chow Ring ◽  
Open Set

This chapter considers varieties whose Chow ring has special properties. This includes abelian varieties, K3 surfaces, and Calabi–Yau hypersurfaces in projective space. For K3 surfaces S, it was discovered that they have a canonical 0-cycle o of degree 1 with the property that the product of two divisors of S is a multiple of o in CH₀(S). This result would later be extended to Calabi–Yau hypersurfaces in projective space. The chapter also considers a decomposition in CH(X × X × X)ℚ of the small diagonal Δ‎ ⊂ X × X × X that was established for K3 surfaces, and is partially extended to Calabi–Yau hypersurfaces. Finally, the chapter uses this decomposition and the spreading principle to show that for families π‎ : X → B of smooth projective K3 surfaces, there is a decomposition isomorphism that is multiplicative over a nonempty Zariski dense open set of B.

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

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

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