scholarly journals Specialness and Isotriviality for Regular Algebraic Foliations

2018 ◽  
Vol 68 (7) ◽  
pp. 2923-2950
Author(s):  
Ekaterina Amerik ◽  
Frédéric Campana
Keyword(s):  
Algebraic Foliations

scholarly journals Some remarks on regular foliations with numerically trivial canonical class

2017 ◽  
Vol Volume 1 ◽  
Author(s):  
Stéphane Druel
Keyword(s):  
Small Rank ◽  
Codimension Two ◽  
Canonical Class ◽  
Special Cases ◽  
Algebraicity Criterion ◽  
Projective Manifolds ◽  
Complex Projective ◽  
Algebraic Foliations

In this article, we first describe codimension two regular foliations with numerically trivial canonical class on complex projective manifolds whose canonical class is not numerically effective. Building on a recent algebraicity criterion for leaves of algebraic foliations, we then address regular foliations of small rank with numerically trivial canonical class on complex projective manifolds whose canonical class is pseudo-effective. Finally, we confirm the generalized Bondal conjecture formulated by Beauville in some special cases. Comment: 20 pages

Complex Algebraic Foliations

2020 ◽  
Author(s):  
Alcides Lins Neto ◽  
Bruno Scárdua
Keyword(s):  
Algebraic Foliations

scholarly journals Singular sets of holonomy maps for algebraic foliations

2013 ◽  
Vol 15 (3) ◽  
pp. 1067-1099 ◽  
Author(s):  
Gabriel Calsamiglia ◽  
Bertrand Deroin ◽  
Sidney Frankel ◽  
Adolfo Guillot
Keyword(s):  
Singular Sets ◽  
Algebraic Foliations

scholarly journals On transcendental automorphisms of algebraic foliations

2003 ◽  
Vol 179 (2) ◽  
pp. 179-190
Author(s):  
B. Scárdua
Keyword(s):  
Algebraic Foliations

scholarly journals ALGEBRAIC FOLIATIONS DEFINED BY QUASI-LINES

2011 ◽  
Vol 22 (10) ◽  
pp. 1501-1528
Author(s):  
LAURENT BONAVERO ◽  
ANDREAS HÖRING
Keyword(s):  
Projective Space ◽  
Singular Locus ◽  
Projective Manifold ◽  
Line Passing ◽  
Rational Fibration ◽  
Algebraic Foliations

Let X be a projective manifold containing a quasi-line l. An important difference between quasi-lines and lines in the projective space is that in general there is more than one quasi-line passing through two given general points. In this paper, we use this feature to construct an algebraic foliation associated to a family of quasi-lines. We prove that if the singular locus of this foliation is not too large, it induces a rational fibration on X that maps the general leaf of the foliation onto a quasi-line in a rational variety.

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