2012/10/22 by Pereira, Jorge Vitorio, Touzet, Frederic · 1 citation
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1210.5916
In this paper we aim at the description of foliations having tangent sheaf T\mathcal F with c1(T\mathcal F)=c2(T\mathcal F)=0 on non-uniruled projective manifolds. We prove that the universal covering of the ambient manifold splits as a product, and that the Zariski closure of a general leaf of \mathcal F is an Abelian variety. It turns out that the analytic type of the Zariski closures of leaves may vary from leaf to leaf. We discuss how this variation is related to arithmetic properties of the tangent sheaf of the foliation.