scholarly journals Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes

1999 ◽  
Vol 127 (9) ◽  
pp. 2633-2642 ◽  
Author(s):  
F. Campana ◽  
B. Kreußler
Keyword(s):  
Projective Planes ◽  
Twistor Spaces ◽  
Connected Sum ◽  
Algebraic Dimension ◽  
Complex Projective

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.

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

scholarly journals Real Hypersurfaces of Nonflat Complex Projective Planes Whose Jacobi Structure Operator Satisfies a Generalized Commutative Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Theocharis Theofanidis
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Additional Restriction ◽  
Real Hypersurfaces ◽  
Specific Function ◽  
Complex Projective Plane ◽  
Jacobi Structure ◽  
Complex Projective

Real hypersurfaces satisfying the conditionϕl=lϕ(l=R(·,ξ)ξ)have been studied by many authors under at least one more condition, since the class of these hypersurfaces is quite tough to be classified. The aim of the present paper is the classification of real hypersurfaces in complex projective planeCP2satisfying a generalization ofϕl=lϕunder an additional restriction on a specific function.

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 Unobstructedness of hyperkähler twistor spaces

2021 ◽  
Author(s):  
Ana-Maria Brecan ◽  
Tim Kirschner ◽  
Martin Schwald
Keyword(s):  
Open Neighborhood ◽  
Projective Line ◽  
Twistor Spaces ◽  
Period Map ◽  
Universal Family ◽  
Complex Projective Line ◽  
Complex Projective

AbstractA family of irreducible holomorphic symplectic (ihs) manifolds over the complex projective line has unobstructed deformations if its period map is an embedding. This applies in particular to twistor spaces of ihs manifolds. Moreover, a family of ihs manifolds over a subspace of the period domain extends to a universal family over an open neighborhood in the period domain.

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