Quarto-quartic birational maps of ℙ3(ℂ)

2017 ◽  
Vol 28 (05) ◽  
pp. 1750037
Author(s):  
Julie Déserti ◽  
Frédéric Han
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Birational Maps ◽  
Dimension Formula ◽  
Trigonal Curves ◽  
Irreducible Components ◽  
Genus Formula ◽  
Complex Projective

We construct a determinantal family of quarto-quartic transformations of a complex projective space of dimension [Formula: see text] from trigonal curves of degree [Formula: see text] and genus [Formula: see text]. Moreover, we show that the variety of [Formula: see text]-birational maps of [Formula: see text] has at least four irreducible components and describe three of them.

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

Reduction theorem of the codimension of minimal generic submanifolds in a complex projective space

1995 ◽  
Vol 54 (2) ◽  
pp. 137-143
Author(s):  
Sung-Baik Lee ◽  
Seung-Gook Han ◽  
Nam-Gil Kim ◽  
Masahiro Kon
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Reduction Theorem ◽  
Generic Submanifolds ◽  
Complex Projective

Hermitian–Einstein metrics and jumping lines forSp(n+1)-homogeneous bundles over ℙ2n+1

1993 ◽  
Vol 114 (3) ◽  
pp. 443-451
Author(s):  
Al Vitter
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Vector Bundles ◽  
Einstein Metrics ◽  
Einstein Metric ◽  
Holomorphic Vector Bundles ◽  
Kähler Form ◽  
Points Of View ◽  
The Stability ◽  
Complex Projective

Stable holomorphic vector bundles over complex projective space ℙnhave been studied from both the differential-geometric and the algebraic-geometric points of view.On the differential-geometric side, the stability ofE-→ ℙncan be characterized by the existence of a unique hermitian–Einstein metric onE, i.e. a metric whose curvature matrix has trace-free part orthogonal to the Fubini–Study Kähler form of ℙn(see [6], [7], and [13]). Very little is known about this metric in general and the only explicit examples are the metrics on the tangent bundle of ℙnand the nullcorrelation bundle (see [9] and [10]).

Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie 𝔻-parallel

2013 ◽  
Vol 56 (2) ◽  
pp. 306-316 ◽  
Author(s):  
Juan de Dios Pérez ◽  
Young Jin Suh
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Jacobi Operator ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
Complex Projective

AbstractWe prove the non-existence of real hypersurfaces in complex projective space whose structure Jacobi operator is Lie 𝔻-parallel and satisfies a further condition.

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