ﻻ يوجد ملخص باللغة العربية
Given a (singular, codimension 1) holomorphic foliation F on a complex projective manifold X, we study the group PsAut(X, F) of pseudo-automorphisms of X which preserve F ; more precisely, we seek sufficient conditions for a finite index subgroup of PsAut(X, F) to fix all leaves of F. It turns out that if F admits a (possibly degenerate) transverse hyperbolic structure , then the property is satisfied; furthermore, in this setting we prove that all entire curves are algebraically degenerate. We prove the same result in the more general setting of transversely projective foliations, under the additional assumptions of non-negative Kodaira dimension and that for no generically finite morphism f : X $rightarrow$ X the foliation f*F is defined by a closed rational 1-form.
We study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of such foliations by curves up to degree 3,
We introduce a notion of normal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this normal form exists and is unique when ambient space is two-dimensional. From this result o
We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree at most 2
We study the branched holomorphic projective structures on a compact Riemann surface $X$ with a fixed branching divisor $S, =, sum_{i=1}^d x_i$, where $x_i ,in, X$ are distinct points. After defining branched ${rm SO}(3,{mathbb C})$--opers, we show t
We give a simplified proof (in characteristic zero) of the decomposition theorem for complex projective varieties with klt singularities and numerically trivial canonical bundle. The proof rests in an essential way on most of the partial results of t