Bounds on leaves of one-dimensional foliations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Bounds on leaves of one-dimensional foliations

Authors:

Affiliation:

(1) IMPA, Estrada D. Castorina 110, 22460–320 Rio de Janeiro RJ, BRAZIL;(2) Math Dept, Room 2-278 MIT, 77 Mass Ave, Cambridge, MA 02139-4307, USA

Abstract:

Let X be a variety overan algebraically closed field, $eta :Omega ^{1}_{X} to {cal L}$ a onedimensionalsingular foliation, and $$
C subseteq X
$$

a projective leaf of .We prove that

$2p_{a} {left( C right)} - 2 = deg {left( {{cal L}left| C right.} right)} + lambda {left( C right)} - deg {left( {C cap S} right)}$

where p _a(C) is the arithmetic genus, where lambda

(C) is the colength in thedualizing sheaf of the subsheaf generated by the Kählerdifferentials, and where S isthe singular locus of . We bound lambda

, and then improve andextend some recent results of Campillo, Carnicer, and de laFuente, and of du Plessis and Wall.Dedicated to IMPA on the occasion of its 50^th anniversary

Keywords:

: foliations curves singularities

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