Analytic Varieties Invariant by Holomorphic Foliations and Pfaff Systems

Maurício Corrêa ()
Additional contact information
Maurício Corrêa: Dipartimento di Matematica, Università degli Studi di Bari

Chapter Chapter 4 in Handbook of Geometry and Topology of Singularities VI: Foliations, 2024, pp 123-150 from Springer

Abstract: Abstract In this work we shall present a survey on problems and results on singular holomorphic foliations and Pfaff systems on complex manifolds assuming that these objects possess invariant analytic varieties. We will focus on recent results which have been motivated by classical works of Darboux, Poincaré and Painlevé on the problem of algebraic integration of singular polynomial differential equations. We present results on Poincaré and Painlevé problem of bounding the degree and the genus of analytic varieties invariant by holomorphic foliations and Pfaff systems. We shall discuss the general ideas of the theory of integrability characterizing the existence of meromorphic first integrals for complex analytic Pfaff equations.

Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-54172-8_4

Ordering information: This item can be ordered from
http://www.springer.com/9783031541728

DOI: 10.1007/978-3-031-54172-8_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().