叶的可拓性

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-09-25 DOI:10.1016/j.aim.2025.110538

Pablo Perrella , Sebastián Velazquez

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引用次数: 0

摘要

给定X上的叶理F和一个嵌入X，在Y上是否存在扩展F的叶理？利用形式化的方法，我们证明了当嵌入对（X，F）足够正且F的奇点属于某一类时，这个问题有一个肯定的答案。这些工具也适用于Y是x的变形的总空间的情况。关于扩展的唯一性，我们证明了Fujita和Grauert的声明的叶状版本，确保管状邻域的存在。我们也给出了叶化只有平凡展开的充分条件，推广了Gómez-Mont的结果。

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Extendability of foliations

Given a foliation F on X and an embedding

X \subseteq Y

, is there a foliation on Y extending F? Using formal methods, we show that this question has an affirmative answer whenever the embedding is sufficiently positive with respect to

(X, F)

and the singularities of F belong to a certain class. These tools also apply in the case where Y is the total space of a deformation of X. Regarding the uniqueness of the extension, we prove a foliated version of a statement by Fujita and Grauert ensuring the existence of tubular neighborhoods. We also give sufficient conditions for a foliation to have only trivial unfoldings, generalizing a result due to Gómez-Mont.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.