共查询到20条相似文献,搜索用时 62 毫秒
1.
In this paper we provide sufficient conditions for maps of vector bundles on smooth projective varieties to be uniquely determined by their degeneracy schemes. We then specialize to holomorphic distributions and foliations. In particular, we provide sufficient conditions for foliations of arbitrary rank on $\mathbb P ^n$ to be uniquely determined by their singular schemes. 相似文献
2.
In these introductory notes we give the basics of the theory of holomorphic foliations and laminations. The emphasis is on the theory of harmonic currents and unique ergodicity for laminations transversally Lipschitz in ?2 and for generic holomorphic foliations in ?2. 相似文献
3.
We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these objects. As consequence, we give some applications to holomorphic foliations tangent to real-analytic Levi-flat hypersurfaces with singularities in \(\mathbb {P}^2\). 相似文献
4.
E. M. Chirka 《Proceedings of the Steklov Institute of Mathematics》2006,253(1):212-220
Hartogs’ separate analyticity theorem is extended to functions holomorphic along holomorphic curves that form mutually transversal foliations of the domain of definition of these functions. 相似文献
5.
Dominique Cerveau 《Bulletin of the Brazilian Mathematical Society》2013,44(4):653-679
We propound several problems concerning codimension one holomorphic foliations either in a local context (theory of singularities) or in a global situation (algebraic foliations). Each problem is illustrated by suitable examples. 相似文献
6.
We study the existence and stability of holomorphic foliations in dimension greater than 4 under perturbations of the underlying
almost-complex structure. An example is given to show that, unlike in dimension 4, J-holomorphic foliations are not stable under large perturbations of almost-complex structure. 相似文献
7.
JUN-MUK HWANG 《Compositio Mathematica》1997,105(1):65-77
A zero set of a holomorphic vector field is totally degenerate, if the endomorphism of the conormal sheaf induced by the vector field is identically zero. By studying a class of foliations generalizing foliations of C*-actions, we show that if a projective manifold admits a holomorphic vector field with a smooth totally degenerate zero component,then the manifold is stably birational to that component of the zero set.When the vector field has an isolated totally degenerate zero, we prove that the manifold is rational. This is a special case of Carrell's conjecture. 相似文献
8.
Maurício CorrêaJr. Márcio G. Soares 《Bulletin of the Brazilian Mathematical Society》2011,42(3):485-503
We study one-dimensional holomorphic foliations on products of complex projective spaces and present results giving the number
of singularities, counting multiplicities, of a generic foliation, a criterion for a foliation to be Riccati and a Poincaré
type inequality, relating degrees of foliations to degrees of hypersurfaces which are invariant by them. 相似文献
9.
Luís Gustavo Mendes 《Geometriae Dedicata》2009,139(1):33-47
The idea of the proof of the classical Noether–Fano inequalities can be adapted to the domain of codimension one singular
holomorphic foliations of the projective space. We obtained criteria for proving that the degree of a foliation on the plane
is minimal in the birational class of the foliation and for the non-existence of birational symmetries of generic foliations
(except automorphisms). Moreover, we give several examples of birational symmetries of special foliations illustrating our
results.
相似文献
10.
Kazumi Tsukada 《Geometriae Dedicata》1997,68(1):61-71
We investigate holomorphic maps between compact generalized Hopf manifolds (i.e., locally conformal Kähler manifolds with parallel Lee form). We show that they preserve the canonical foliations. Moreover, we study compact complex submanifolds of g.H. manifolds and holomorphic submersions from compact g.H. manifolds. 相似文献
11.
We classify the holomorphic diffeomorphisms
of complex projective varieties with an Anosov dynamics and
holomorphic stable and unstable foliations: The variety is
finitely covered by a compact complex torus and the diffeomorphism
corresponds to a linear transformation of this torus.
Difféomorphismes holomorphes Anosov相似文献
12.
The aim of this paper is to classify compact, simply connected Kähler manifolds which admit totally geodesic, holomorphic complex homothetic foliations by curves. 相似文献
14.
Bruno Scárdua 《Journal of Pure and Applied Algebra》2011,215(5):764-788
Intuitively, a complex Liouvillian function is one that is obtained from complex rational functions by a finite process of integrations, exponentiations and algebraic operations. In the framework of ordinary differential equations the study of equations admitting Liouvillian solutions is related to the study of ordinary differential equations that can be integrated by the use of elementary functions, that is, functions appearing in the Differential Calculus. A more precise and geometrical approach to this problem naturally leads us to consider the theory of foliations. This paper is devoted to the study of foliations that admit a Liouvillian first integral. We study holomorphic foliations (of dimension or codimension one) that admit a Liouvillian first integral. We extend results of Singer (1992) [20] related to Camacho and Scárdua (2001) [4], to foliations on compact manifolds, Stein manifolds, codimension-one projective foliations and germs of foliations as well. 相似文献
15.
Joan Girbau 《Israel Journal of Mathematics》1981,40(3-4):235-254
In this paper we deal with a complex analytic foliation of a compact complex manifold endowed with a bundle-like metric and
give a transversally holomorphic rigidity theorem (Theorem 9.1) for these foliations, depending on curvature conditions. We
give some examples for which we study holomorphic rigidity. The classical vanishing theorems of Nakano, Griffiths and Le Potier
are the main tools we use to prove our results. 相似文献
16.
Ruben Lizarbe 《Mathematische Nachrichten》2023,296(9):3877-3891
We prove that a generic holomorphic foliation on a weighted projective plane has no algebraic solutions when the degree is big enough. We also prove an analogous result for foliations on Hirzebruch surfaces. 相似文献
17.
18.
Marco Brunella 《Annals of Global Analysis and Geometry》1997,15(2):179-186
We prove a global stability theorem for transversely holomorphic foliations of complex codimension one: if there exists a compact leaf with finite holonomy, then the foliation is a Seifert fibration (that is, every leaf is compact and has finite holonomy). 相似文献
19.
We generalize Frobenius singular theorem due to Malgrange, for a large class of codimension one holomorphic foliations on
singular analytic subsets of ℂ
N
.
This research was partially supported by Pronex. 相似文献
20.
Paul-Andi Nagy 《Journal of Geometric Analysis》2003,13(4):659-667
We study Riemannian foliations with complex leaves on Kähler manifolds. The tensor T, the obstruction to the foliation be totally geodesic, is interpreted as a holomorphic section of a certain vector bundle. This enables us to give classification results when the manifold is compact. 相似文献