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We study a holomorphic analogue of Tischler approximation for closed differential forms normalized by a prescribed holomorphic vector field. The main setting consists of connected normal Stein spaces satisfying a degree-one reflexive Poincar\'e property, with finitely generated first integral homology and a holomorphic...
In this work, we study analytic deformations of a pencil [Formula: see text] where [Formula: see text] and [Formula: see text] are holomorphic functions defined in [Formula: see text], and [Formula: see text] are relatively prime integers. We consider analytic deformations given by integrable [Formula: see text]-forms...
We study rigidity phenomena for holomorphic foliations associated with irreducible cuspidal cubics. If $C\subset\PP^2$ is such a cubic, we denote by $p$ its cusp and by $q$ its unique smooth inflection point (or flex), where the tangent line has contact of order three with the cubic. Our first main result is an intrins...
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