Number Variance of Random Zeros on Complex Manifolds

2008 ◽  
Vol 18 (4) ◽  
pp. 1422-1475 ◽  
Author(s):  
Bernard Shiffman ◽  
Steve Zelditch
Keyword(s):  
Complex Manifolds ◽  
Random Zeros

scholarly journals Overcrowding and hole probabilities for random zeros on complex manifolds

2008 ◽  
Vol 57 (5) ◽  
pp. 1977-1998 ◽  
Author(s):  
Bernard Shiffman ◽  
Steve Zelditch ◽  
Scott Zrebiec
Keyword(s):  
Complex Manifolds ◽  
Random Zeros ◽  
Hole Probabilities

scholarly journals Convergence of random zeros on complex manifolds

2008 ◽  
Vol 51 (4) ◽  
pp. 707-720 ◽  
Author(s):  
Bernard Shiffman
Keyword(s):  
Complex Manifolds ◽  
Random Zeros

scholarly journals Number Variance of Random Zeros on Complex Manifolds, II: Smooth Statistics

2010 ◽  
Vol 6 (4) ◽  
pp. 1145-1168 ◽  
Author(s):  
Bernard Shiffman ◽  
Steve Zelditch
Keyword(s):  
Complex Manifolds ◽  
Random Zeros

A characterization of complex manifolds biholomorphic to a circular domain

1985 ◽  
Vol 189 (3) ◽  
pp. 343-363 ◽  
Author(s):  
Giorgio Patrizio
Keyword(s):  
Circular Domain ◽  
Complex Manifolds

scholarly journals On contact structures of real and complex manifolds

1963 ◽  
Vol 15 (3) ◽  
pp. 227-252 ◽  
Author(s):  
Seizi Takizawa
Keyword(s):  
Contact Structures ◽  
Complex Manifolds

scholarly journals Schottky groups acting on homogeneous rational manifolds

2019 ◽  
Vol 2019 (753) ◽  
pp. 23-56 ◽  
Author(s):  
Christian Miebach ◽  
Karl Oeljeklaus
Keyword(s):  
Deformation Theory ◽  
Group Actions ◽  
Picard Group ◽  
Schottky Group ◽  
Fundamental Groups ◽  
Complex Manifolds ◽  
Schottky Groups ◽  
Algebraic Dimension ◽  
Geometric Invariants ◽  
Compact Complex Manifolds

AbstractWe systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori’s well-known construction. This yields new examples of non-Kähler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to Lárusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of {{\rm{SL}}(2,\mathbb{C})/\Gamma} for Γ a discrete free loxodromic subgroup of {{\rm{SL}}(2,\mathbb{C})}, previously obtained by A. Guillot.

scholarly journals Higher-page Bott–Chern and Aeppli cohomologies and applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dan Popovici ◽  
Jonas Stelzig ◽  
Luis Ugarte
Keyword(s):  
Positive Integer ◽  
Spectral Sequence ◽  
Complex Manifolds ◽  
Serre Duality ◽  
Frölicher Spectral Sequence ◽  
Compact Complex Manifolds

Abstract For every positive integer r, we introduce two new cohomologies, that we call E r {E_{r}} -Bott–Chern and E r {E_{r}} -Aeppli, on compact complex manifolds. When r = 1 {r\kern-1.0pt=\kern-1.0pt1} , they coincide with the usual Bott–Chern and Aeppli cohomologies, but they are coarser, respectively finer, than these when r ≥ 2 {r\geq 2} . They provide analogues in the Bott–Chern–Aeppli context of the E r {E_{r}} -cohomologies featuring in the Frölicher spectral sequence of the manifold. We apply these new cohomologies in several ways to characterise the notion of page- ( r - 1 ) {(r-1)} - ∂ ⁡ ∂ ¯ {\partial\bar{\partial}} -manifolds that we introduced very recently. We also prove analogues of the Serre duality for these higher-page Bott–Chern and Aeppli cohomologies and for the spaces featuring in the Frölicher spectral sequence. We obtain a further group of applications of our cohomologies to the study of Hermitian-symplectic and strongly Gauduchon metrics for which we show that they provide the natural cohomological framework.

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