arXiv 0907.31402009-07-17math.CVmath.DG

由具有一般切锥的函数定义的叶理和曲线的Normal forms

Normal forms of foliations and curves defined by a function with a generic tangent cone

Yohann Genzmer, Emmanuel Paul

摘要：

我们首先描述的本地和全球的芽叶理定义的解析函数在两个变量的p横向光滑分支，并与积分的多重性（在单值全纯的情况下）或复杂的多重性（在多值“达布”的情况下）的模空间。我们在每个类中指定标准形式。然后在这些模空间上研究了由以下等价关系导出的分布C：两点等价当且仅当对应的叶理在解析共轭下具有相同的解析不变曲线。因此，C的叶空间是曲线的模空间。我们证明了C是有理可积的。这些有理积分给出了这些一般平面曲线的完整的不变量系统，它扩展了分支之间的公知交比。

英文摘要：

We first describe the local and global moduli spaces of germs of foliations defined by analytic functions in two variables with p transverse smooth branches, and with integral multiplicities (in the univalued holomorphic case) or complex multiplicities (in the multivalued ''Darboux'' case). We specify normal forms in each class. Then we study on these moduli space the distribution C induced by the following equivalence relation: two points are equivalent if and only if the corresponding foliations have the same analytic invariant curves up to analytical conjugacy. Therefore, the space of leaves of C is the moduli space of curves. We prove that C is rationally integrable. These rational integrals give a complete system of invariants for these generic plane curves, which extend the well-known cross-ratios between branches.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

摘要英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Holomorphic foliations tangent to Levi-flat subsets

We study Segre varieties associated to Levi-flat subsets in complex manifolds and apply them to establish local and global results on the integration of tangent holomorphic foliations.

2017-05-26math.CVmath.DS

与Levi-平坦超曲面相切的$\mathbb{P}^n$中叶理的动力学

On the dynamics of foliations in $\mathbb{P}^n$ tangent to Levi-flat hypersurfaces

设$\mathcal{F}$是$\mathbb{P}^n$中的余维1的全纯叶理，$n\geq 2$，其不变式为具有正则部分$M^{*}$的实解析Levi平坦超曲面$M$.然后，$\overline{M^{*}}$外的每个$\mathcal{F}$叶在$\overline{M^{*}}$中积累。

2014-03-19math.CV

与Rolle-Pfaffian超曲面相切的全纯叶状结构

Holomorphic foliations tangent to Rolle-pfaffian hypersurfaces

本文研究复平面原点处满足Rolle-Khovanskii条件的与Pfaffian超曲面相切的全纯叶状结构芽，证明其由闭亚纯1-形式定义，并完成奇点消解中简单模型的分类。

2024-08-07math.CVmath.DS

Holomorphic vector fields tangent to foliations in dimension three

This article studies germs of holomorphic vector fields at the origin of C3 that are tangent to holomorphic foliations of codimension one. Two situations are considered. First, we assume hypotheses on the reduction of singularities of the vector field - for instance, that the final models belong to a family of vector fields whose linear parts have eigenvalues satisfying a condition of non-resonance - in order to conclude that the foliation is of complex hyperbolic type, that is, without saddle-nodes in its reduction of singularities. In the second part, we prove that a vector field that is tan…

2018-12-06math.CAmath.CVmath.DS

切层分裂的全纯叶解的稳定性

Stability of Holomorphic Foliations with Split Tangent Sheaf

证明了具有分裂切层且具有好奇异集的射影空间的奇异全纯叶理集在全纯叶理空间中是开的。作为应用，我们推广了Camacho-Lins Neto关于线性拉回叶理的一个结果，给出了余维$k \ge 2$的$\mathcal L$ -叶理的刚性的一个判别准则，并证明了Cerveau-Litti关于$\mathbb P^4$的余维1的$\mathcal L$ -叶理的刚性的一个猜想.这些结果使我们能够展示一些以前未知的奇异全纯叶理空间的不可约分量。

2007-03-19math.AGmath.CVmath.DS

Lipschitz normally embedded set and tangent cones at infinity

We prove that any analytic set in $\C^n$ with a unique tangent cone at infinity is an algebraic set. We prove that the degree of a complex algebraic set in $\C^n$, which is Lipschitz normally embedded at infinity, is equal to the degree of its tangent cone at infinity.

2021-03-22math.CVmath.DG

更多相关论文收起更多论文

Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations

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 $\mathbb{P}^2$.

2017-11-28math.CV

Singular holomorphic foliations by curves II: Negative Lyapunov exponent

Let \Fc be a holomorphic foliation by Riemann surfaces defined on a compact complex projective surface X satisfying the following two conditions: (1) the singular points of \Fc are all hyperbolic; (2) \Fc is Brody hyperbolic. Then we establish cohomological formulas for the Lyapunov exponent and the Poincaré mass of an extremal positive \ddc-closed current tangent to \Fc. If, moreover, there is no nonzero positive closed current tangent to \Fc, then we show that the Lyapunov exponent χ(\Fc) of \Fc, which is, by definition, the Lyapunov exponent of the unique normalized positive \ddc-closed cur…

2020-05-29math.CVmath.DS

环形分解与在双曲锥面Teichmüller空间上的剪切半径坐标

Circular foliations and shear-radius coordinates on Teichmüller spaces of hyperbolic cone surfaces

本文研究了双曲锥面Teichmüller空间上的环形分解与剪切半径坐标，通过构造适应测地三角互补区域的分解，定义了剪切和半径参数，并给出了相关变形和收敛性结果。

2025-12-24math.CVmath.DGmath.GT

关于多重次谐波电流的切锥

On the tangent cones to plurisubharmonic currents

本文在适当的条件下研究了正的多重次谐波或多重超谐波流切锥的存在性。给出了与电流及其$dd^c$相关的Lelong函数的增长性的估计，以保证该电流爆破的存在性.切锥的存在性的第二个证明来自这些估计。

2011-12-15math.CV

Tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. Appendix by Anne Pichon and Walter D. Neumann

We prove that tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. We also extend to real subanalytic sets the notion of reduced tangent cone and we show that subanalytic Lipschitz normally embedded sets have reduced tangent cones. In particular, we get that Lipschitz normally embedded complex analytic sets have reduced tangent cones.

2017-08-19math.AGmath.CV

二次全纯叶形及其任意维数

Holomorphic foliations of degree two and arbitrary dimension

Dipartimento di Matematica, Università degli Studi di Bari（巴里大学数学系）；Universidade Estadual de Campinas (UNICAMP) Instituto de Matemática, Estatística e Computação Científica (IMECC) Departamento de Matemática（坎皮纳斯州立大学数学、统计与科学计算研究所数学系）；Departamento de Matemática Centro de Ciências Exatas e da Natureza Universidade Federal de Pernambuco（伯南布哥联邦大学自然与精确科学中心数学系）

本文研究了二次全纯叶形在任意维度上的分类，证明了其分类结果并探讨了相关泊松结构的几何特性。

2026-01-19math.AGmath.CVmath.DS

Degeneracy of entire curves into higher dimensional complex manifolds

Pursuing McQuillan's philosophy in proving the Green-Griffiths conjecture for certain surfaces of general type, we deal with the algebraic degeneracy of entire curves tangent to holomorphic foliations by curves. Inspired by the recent work of Paun and Sibony, we study the intersection of Ahlfors current with the tangent bundle of the foliation, and derive some consequences. In particular, we introduce the definition of weakly reduced singularities for foliations by curves, which requires less work than the exact classification for foliations. Finally we discuss the strategy to prove the Green-…

2016-03-07math.AGmath.CV

正电流方向切锥的存在性

Existence of the directional tangent cone to a positive current

本文首先证明了正电流$T$的严格变换的存在性，只要它的$j^{th}$电流$T_j$是多次谐波或多超谐波。然后，在$T_j$的适当条件下，证明了$T$的有向切锥的存在性.在特殊情况下，当$T$是封闭的，我们给第二个条件独立于前一个。

2012-12-23math.CV

Averaged mixed Julia-Fatou type theory with applications to spectral foliation

Classically, theorems of Fatou and Julia describe the boundary regularity of functions in one complex variable. The former says that a complex analytic function on the disk has non-tangential boundary values almost everywhere, and the latter describes when a function takes an extreme value at a boundary point and is differentiable there non-tangentially. We describe a class of intermediate theorems in terms of averaged Julia-Fatou quotients. Boundary regularity is related to integrability of certain quantities against a special measure, the so-called Nevanlinna measure. Applications are given …

2021-08-19math.CVmath.FAmath.SP

切锥与实超曲面的正则性

Tangent cones and regularity of real hypersurfaces

我们刻画了$\R^n$的嵌入$\C^1$超曲面为唯一的具有连续变化的平坦切锥的局部闭集，其测度理论重数至多为$m<3/2$。因此，任何（拓扑）超曲面，它具有平坦的切锥，并且处处由均匀半径的球支撑，是$\C^1$。在实解析情形中，在每个切锥是超曲面的弱化假设下，同样的结论也成立。特别地，任何凸实解析超曲面$X\subset\R^n$都是$\C^1$。此外，如果$X$是实代数的、严格凸的和无界的，则它的射影闭包也是$\C^1$超曲面，这表明$X$是定义在整个超平面上的函数的图。

2013-09-14math.AGmath.CVmath.DG

三维情形中的分布与Legendre叶状结构

Distributions and Legendrian foliations in dimension 3

研究3维流形上分布的有理首次积分场，证明了存在具有相同首次积分场的切向量场，并将类似结果推广至任意维数的可积分布。

2024-06-25math.AGmath.CV

Codimension one holomorphic distributions on the projective three-space

We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree at most 2 with locally free tangent sheaves, and show that codimension one distributions of arbitrary degree with only isolated singularities have stable tangent sheaves. Furthermore, we describe the moduli space of distributions in terms of Grothendieck's Quot-scheme for the tangent bundle. In certain cases, we show that the moduli space of codimension one …

2018-09-30math.AGmath.CVmath.DG

Some classes of homeomorphisms that preserve multiplicity and tangent cones

In this paper we present some applications of A'Campo-Lê's Theorem and we study some relations between Zariski's Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant when we consider right equivalence and this class contains many known classes of homeomorphisms that preserve tangent cones. In particular, we present some effective approaches to Zariski's Question A. We show a version of these results looking at infinity. Add…

2019-11-19math.AGmath.CV

加权射影空间上叶状结构的拉回的稳定性

Stability of pullbacks of foliations on weighted projective spaces

该研究证明了加权射影空间上带分裂切层的叶状结构的拉回所对应的射影空间叶状结构的稳定性定理，可构造多个新的叶状结构空间不可约分支，并为其他叶状结构族的稳定性提供统一替代证明。

2025-01-13math.AGmath.CVmath.DS

关于叶状结构的第二陈类的注记

Remarks on the second Chern class of a foliation

Universidade Federal de Pernambuco（伯南布哥联邦大学）

本文研究了叶状结构的第二陈类及其奇点方案的度数，提出对于射影空间上的叶状结构，其奇点方案的度数下界为d+1，并探讨了等号成立的条件。

2026-01-18math.AGmath.CV