On codimension 1 families of singular meromorphic foliations having a meromorphic first integral

✍ Scribed by E. Ballico

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 143 KB
• Volume: 111
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00217-5

✦ Synopsis

Let X ⊂ CP N be a smooth compact complex manifold. Here we study certain codimension 1 holomorphic foliations with singularities on X cut out by a pencil of hyperplanes through a codimension 2 linear subspace of CP N . We classify the codimension 1 strata of the closure, M, of the foliations on X induced by Lefschetz pencils. Under certain cohomological assumptions we describe M. For certain X we study also a few related holomorphic singular foliations of higher codimension.