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摘要翻译：
同维一叶网是有限多个同维一叶在一般位置上的构型。许多经典理论都是围绕阿贝尔关系的概念发展而来的：阿贝尔关系是定义网络的叶层的第一个积分之间的函数关系，让人想起经典代数几何中的阿贝尔加法定理。给定网络的阿贝尔关系形成一个有限维向量空间，其维数（网络的秩）以Castelnuovo数p(n，k)为界，其中n是周围空间的维数，k是定义网络的树叶数。腹板几何中的一个基本问题是异常腹板的分类，即极大秩的腹板不等价于射影曲线的对偶。最近，J.-M.Trepreau证明了对于n>2和k>2n-1没有例外的k网。在维数2中，对于任意k有例外的k-网的例子，分类问题是开放的。本文对定义在紧致复杂曲面上的例外完全可分解拟线性(CDQL)网进行了全局分类。根据定义，CDQL(k+1)-网由k个线性叶理和一个非线性叶理叠加而成。例如，我们证明了直到射影变换，在射影平面上有四个可数族和十三个零星例外CDQL网。
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英文标题：
《The Classification of Exceptional CDQL Webs on Compact Complex Surfaces》
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作者：
Jorge Vitorio Pereira, Luc Pirio
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Codimension one webs are configurations of finitely many codimension one foliations in general position. Much of the classical theory evolved around the concept of abelian relation: a functional relation among the first integrals of the foliations defining the web reminiscent of Abel's addition theorem in classical algebraic geometry. The abelian relations of a given web form a finite dimensional vector space with dimension (the rank of the web) bounded by Castelnuovo number p(n,k) where n is the dimension of the ambient space and k is the number of foliations defining the web. A fundamental problem in web geometry is the classification of exceptional webs, that is, webs of maximal rank not equivalent to the dual of a projective curve. Recently, J.-M. Trepreau proved that there are no exceptional k-webs for n>2 and k > 2n-1. In dimension two there are examples of exceptional k-webs for arbitrary k and the classification problem is wide open. In this paper, we classify the exceptional Completely Decomposable Quasi-Linear (CDQL) webs globally defined on compact complex surfaces. By definition, the CDQL (k+1)-webs are formed by the superposition of k linear foliations and one non-linear foliation. For instance, we show that up to projective transformations there are exactly four countable families and thirteen sporadic exceptional CDQL webs on the projective plane.
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PDF链接：
https://arxiv.org/pdf/0806.3290
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