HOLOMORPHIC FOLIATIONS AND CHARACTERISTIC NUMBERS

2005 ◽  
Vol 07 (05) ◽  
pp. 583-596 ◽  
Author(s):  
MARCIO G. SOARES
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Holomorphic Foliation ◽  
Compact Complex Manifold ◽  
Holomorphic Foliations ◽  
Singular Set ◽  
One Dimensional ◽  
Characteristic Numbers ◽  
Complex Projective

We relate the characteristic numbers of the normal sheaf of a k-dimensional holomorphic foliation [Formula: see text] of a compact complex manifold Mn, to the characteristic numbers of the normal sheaf of a one-dimensional holomorphic foliation associated to [Formula: see text]. In case M is a complex projective space, we also obtain bounds for the degrees of the components of codimension k - 1 of the singular set of [Formula: see text].

scholarly journals On the geometry of Poincaré's problem for one-dimensional projective foliations

2001 ◽  
Vol 73 (4) ◽  
pp. 475-482 ◽  
Author(s):  
MARCIO G. SOARES
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Projective Variety ◽  
Holomorphic Foliation ◽  
One Dimensional ◽  
Complex Projective Variety ◽  
Geometric Objects ◽  
Complex Projective

We consider the question of relating extrinsic geometric characters of a smooth irreducible complex projective variety, which is invariant by a one-dimensional holomorphic foliation on a complex projective space, to geometric objects associated to the foliation.

Remarks on Kähler–Ricci solitons

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Lucio Bedulli ◽  
Anna Gori
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Ricci Soliton ◽  
Compact Complex Manifold ◽  
Ricci Solitons ◽  
Complex Projective

AbstractWe prove that a compact complex manifold endowed with a Kähler-Ricci soliton cannot be isometrically embedded in a complex projective space ℂℙ

A Big Picard Theorem for Holomorphic Maps into Complex Projective Space

2009 ◽  
Vol 52 (1) ◽  
pp. 154-160
Author(s):  
Yasheng Ye ◽  
Min Ru
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Holomorphic Maps ◽  
Analytic Subvariety ◽  
Picard Theorem ◽  
Complex Projective

AbstractWe prove a big Picard type extension theoremfor holomorphic maps f : X–A → M, where X is a complex manifold, A is an analytic subvariety of X, and M is the complement of the union of a set of hyperplanes in ℙn but is not necessarily hyperbolically imbedded in ℙn.

scholarly journals DEGENERATION OF ENDOMORPHISMS OF THE COMPLEX PROJECTIVE SPACE IN THE HYBRID SPACE

2018 ◽  
Vol 19 (4) ◽  
pp. 1141-1183 ◽  
Author(s):  
Charles Favre
Keyword(s):  
Dynamical System ◽  
Projective Space ◽  
Complex Projective Space ◽  
Blow Up ◽  
Equilibrium Measure ◽  
Maximal Entropy ◽  
One Dimensional ◽  
Hybrid Space ◽  
Complex Projective ◽  
Measure Of Maximal Entropy

We consider a meromorphic family of endomorphisms of degree at least 2 of a complex projective space that is parameterized by the unit disk. We prove that the measure of maximal entropy of these endomorphisms converges to the equilibrium measure of the associated non-Archimedean dynamical system when the system degenerates. The convergence holds in the hybrid space constructed by Berkovich and further studied by Boucksom and Jonsson. We also infer from our analysis an estimate for the blow-up of the Lyapunov exponent near a pole in one-dimensional families of endomorphisms.

RUANG PROYEKTIF KOMPLEKS 〖CP〗^n ADALAH MANIFOLD KOMPLEKS

2021 ◽  
Vol 9 (1) ◽  
pp. 99
Author(s):  
Denik Agustito ◽  
Irham Taufiq ◽  
Dafid Slamet Setiana ◽  
Riawan Yudi Purwoko
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Research Method ◽  
Compact Manifold ◽  
Complex Projective Space ◽  
Coherent Sheaves ◽  
Complex Projective

<p>The purpose of this paper to determine the complex projective space  as a complex manifold is to calculate the cohomology of the coherent sheaves of . The research method in this paper is to construct an -dimensional complex projective space, namely  and then the n-dimensional complex projective space, namely , is a complex manifold. The result of this research is the -dimensional complex projective space, namely is a complex and compact manifold.</p>

scholarly journals Singular Levi-flat hypersurfaces in complex projective space induced by curves in the Grassmannian

2015 ◽  
Vol 26 (05) ◽  
pp. 1550036 ◽  
Author(s):  
Jiří Lebl
Keyword(s):  
Algebraic Curve ◽  
Complex Projective Space ◽  
First Integral ◽  
Holomorphic Foliation ◽  
Singular Set ◽  
Analytic Subvariety ◽  
Codimension One ◽  
Real Analytic ◽  
Complex Cone ◽  
Complex Projective

Let H ⊂ ℙn be a real-analytic subvariety of codimension one induced by a real-analytic curve in the Grassmannian G(n + 1, n). Assuming H has a global defining function, we prove H is Levi-flat, the closure of its smooth points of top dimension is a union of complex hyperplanes, and its singular set is either of dimension 2n - 2 or dimension 2n - 4. If the singular set is of dimension 2n - 4, then we show the hypersurface is algebraic and the Levi-foliation extends to a singular holomorphic foliation of ℙn with a meromorphic (rational of degree 1) first integral. In this case, H is in some sense simply a complex cone over an algebraic curve in ℙ1. Similarly if H has a degenerate singularity, then H is also algebraic. If the dimension of the singular set is 2n - 2 and is nondegenerate, we show by construction that the hypersurface need not be algebraic nor semialgebraic. We construct a Levi-flat real-analytic subvariety in ℙ2 of real codimension 1 with compact leaves that is not contained in any proper real-algebraic subvariety of ℙ2. Therefore a straightforward analogue of Chow's theorem for Levi-flat hypersurfaces does not hold.

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