scholarly journals On the neighbourhood of a Hopf surface

1981 ◽  
Vol 57 (7) ◽  
pp. 359-362
Author(s):  
Hajime Tsuji
Keyword(s):  
Hopf Surface

Integrable Systems Associated to a Hopf Surface

2003 ◽  
Vol 55 (3) ◽  
pp. 609-635 ◽  
Author(s):  
Ruxandra Moraru
Keyword(s):  
Elliptic Curve ◽  
Moduli Spaces ◽  
Symplectic Geometry ◽  
Vector Bundles ◽  
Integrable Hamiltonian System ◽  
Complex Surface ◽  
Point Of View ◽  
Infinite Cyclic Group ◽  
Completely Integrable Hamiltonian System ◽  
Hopf Surface

AbstractA Hopf surface is the quotient of the complex surface by an infinite cyclic group of dilations of . In this paper, we study the moduli spaces of stable -bundles on a Hopf surface , from the point of view of symplectic geometry. An important point is that the surface is an elliptic fibration, which implies that a vector bundle on can be considered as a family of vector bundles over an elliptic curve. We define a map that associates to every bundle on a divisor, called the graph of the bundle, which encodes the isomorphism class of the bundle over each elliptic curve. We then prove that the map G is an algebraically completely integrable Hamiltonian system, with respect to a given Poisson structure on . We also give an explicit description of the fibres of the integrable system. This example is interesting for several reasons; in particular, since the Hopf surface is not Kähler, it is an elliptic fibration that does not admit a section.

scholarly journals Pseudoconvex domains in the Hopf surface

2015 ◽  
Vol 67 (1) ◽  
pp. 231-273 ◽  
Author(s):  
Norman LEVENBERG ◽  
Hiroshi YAMAGUCHI
Keyword(s):  
Pseudoconvex Domains ◽  
Hopf Surface
Sign in / Sign up

Export Citation Format

Share Document