Speaker: Javier Gargiulo
Title: Rational pull-backs of toric foliations
Date: 10:30 26/06/2020
Abstract:
In this talk we will present a short digression about the theory of singular foliations on toric varieties and their associated moduli spaces using the Cox quotient construction. In particular, we will construct families of singular projective foliations that arise as pull-backs of foliations on a complete simplicial toric variety X by a suitable family of rational maps from a classical projective space to X. We will focus on the following:
1. Singular projective foliations of codimension dim(X) induced by the fibers of rational maps from a projective space to X.
2. Singular projective foliations of codimension one which are pull-backs of a foliation on a toric surface.
In the first part, we will show exactly which are the cases where these foliations fill out irreducible components of the corresponding moduli space. As for the second type of foliations, we will describe certain aspects of their singular scheme and their first order unfoldings and deformations.
References:
1] Cox, D.A., Little, J.B. and Schenck, H.K. Toric varieties. American Mathematical Society (2011).
[2] Cerveau, D., Lins Neto, A. and Edixhoven, S.J. Pull-back components of the space of holomorphic foliations on CP (n), n ≥ 3. Journal of Algebraic Geometry, vol. 10, no. 4, p. 695-711 (2001).
[3] Gargiulo Acea, J. Logarithmic forms and singular projective foliations. Annales de l’institut Fourier, Tome 70, no. 1, p. 171-203 (2019).
[4] Gargiulo Acea, J., Molinuevo, A. and Velazquez, S. Rational pull-backs of toric foliations. In preparation (2020).
[5] Massri, C., Moliuevo, A. and Quallbrunn, F. The Kupka scheme and unfoldings. Asian Journal of Mathematics (2017).