scholarly journals Twistor spaces of algebraic dimension two associated to a connected sum of projective planes

2004 ◽  
Vol 140 (04) ◽  
pp. 1097-1111 ◽  
Author(s):  
Akira Fujiki
Keyword(s):  
Projective Planes ◽  
Twistor Spaces ◽  
Connected Sum ◽  
Algebraic Dimension

scholarly journals Geometry of some twistor spaces of algebraic dimension one

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Nobuhiro Honda
Keyword(s):  
Twistor Space ◽  
Projective Planes ◽  
Canonical System ◽  
K3 Surface ◽  
Twistor Spaces ◽  
Algebraic Dimension ◽  
General Fiber ◽  
Algebraic Reduction ◽  
Dimension One ◽  
Complex Projective

AbstractIt is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is induced by the anti-canonical system of the twistor spaces. It is also shown that the former kind of twistor spaces contain a pair of non-normal Hopf surfaces.

Algebraic dimension of twistor spaces

1988 ◽  
Vol 282 (4) ◽  
pp. 621-627 ◽  
Author(s):  
Y. Sun Poon
Keyword(s):  
Twistor Spaces ◽  
Algebraic Dimension

scholarly journals Four-manifolds up to connected sum with complex projective planes

2022 ◽  
Vol 144 (1) ◽  
pp. 75-118
Author(s):  
Daniel Kasprowski ◽  
Mark Powell ◽  
Peter Teichner
Keyword(s):  
Projective Planes ◽  
Connected Sum ◽  
Four Manifolds ◽  
Complex Projective

On knotted real projective planes

2015 ◽  
Vol 24 (10) ◽  
pp. 1540011
Author(s):  
Yongju Bae ◽  
Seonmi Choi ◽  
Akio Kawauchi
Keyword(s):  
Projective Planes ◽  
Connected Sum ◽  
The Relationship

Let [Formula: see text] be a hyperbolic transformation. Let B be a new band attaching to L such that [Formula: see text] is also a hyperbolic transformation. In this paper, we will study the relationship between the realizing surfaces [Formula: see text] and [Formula: see text]. If B is a noncoherent band to both L and [Formula: see text] such that [Formula: see text] is defined, then [Formula: see text] and [Formula: see text] are ambient isotopic, where RP2 is one of the standard real projective planes. We will study the triviality of [Formula: see text] because as an application, RP2 can untangle some knotted sphere [Formula: see text] with suitable conditions, when it is attached to [Formula: see text] by the connected sum.

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