compact tori
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2020 ◽  
Vol 27 (6) ◽  
pp. 062513
Author(s):  
Carl Dunlea ◽  
Stephen Howard ◽  
Wade Zawalski ◽  
Kelly Epp ◽  
Alex Mossman ◽  
...  

Author(s):  
Kieran G O’Grady

Abstract Dedicato alla piccola Mia. For $X$ a hyperkähler manifold of Kummer type, let $J^3(X)$ be the intermediate Jacobian associated to $H^3(X)$. We prove that $H^2(X)$ can be embedded into $H^2(J^3(X))$. We show that there exists a natural smooth quadric $Q(X)$ in the projectivization of $H^3(X)$, such that Gauss–Manin parallel transport identifies the set of projectivizations of $H^{2,1}(Y)$, for $Y$ a deformation of $X$, with an open subset of a linear section of $Q^{+}(X)$, one component of the variety of maximal linear subspaces of $Q(X)$. We give a new proof of a result of Mongardi restricting the action of monodromy on $H^2(X)$. Lastly, we show that if $X$ is projective, then $J^3(X)$ is an abelian fourfold of Weil type.


2019 ◽  
Vol 2019 (751) ◽  
pp. 121-184 ◽  
Author(s):  
Hiroaki Ishida

AbstractIn this paper, we introduce the notion of maximal actions of compact tori on smooth manifolds and study compact connected complex manifolds equipped with maximal actions of compact tori. We give a complete classification of such manifolds, in terms of combinatorial objects, which are triples {(\Delta,\mathfrak{h},G)} of nonsingular complete fan Δ in {\mathfrak{g}}, complex vector subspace {\mathfrak{h}} of {\mathfrak{g}^{\mathbb{C}}} and compact torus G satisfying certain conditions. We also give an equivalence of categories with suitable definitions of morphisms in these families, like toric geometry. We obtain several results as applications of our equivalence of categories; complex structures on moment-angle manifolds, classification of holomorphic nondegenerate {\mathbb{C}^{n}}-actions on compact connected complex manifolds of complex dimension n, and construction of concrete examples of non-Kähler manifolds.


2017 ◽  
Vol 172 (1-2) ◽  
pp. 119-126 ◽  
Author(s):  
A. Rohollahi ◽  
S. Khatir ◽  
C. Xiao ◽  
A. Hirose
Keyword(s):  

2010 ◽  
Vol 29 (5) ◽  
pp. 447-453 ◽  
Author(s):  
S. Woodruff ◽  
M. Brown ◽  
E. B. Hooper ◽  
R. Milroy ◽  
M. Schaffer
Keyword(s):  

2008 ◽  
Vol 28 (3) ◽  
pp. 275-281 ◽  
Author(s):  
Sh. M. Khalil ◽  
R. A. Altuijri
Keyword(s):  

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