Rational pullbacks of toric foliations

Abstract: In this talk we will present a short digression about the theory of singular foliations on toric varieties and certain algebraic spaces parametrizing them. In particular, we will construct families of singular foliations on a classical projective space that arise as pull-backs of foliations on a simplicial toric variety X under suitable rational maps. We will focus on the case where X is a complete simplicial toric surface.

The singular set of a foliation is one of the most commonly studied geometric objects in the area. The geometry and topology near a singularity characterize (in some sense) the foliation. Not surprisingly, most of the approaches to obtain stability results for singular foliations involve a detailed study of their singular locus. In this respect, we will attempt to describe certain aspects of the singular and Kupka scheme of foliations on a toric surface and their corresponding pull-backs. We will also characterize their first order unfoldings and deformations in some cases.

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

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