# Details of talk

Title | Foliations and webs inducing Galois coverings |
---|---|

Presenter | Marcel Nicolau (Universitat Autonoma de Barcelona) |

Author(s) | Assoc Prof Marcel Nicolau |

Session | n/a |

Time | |

Abstract | This talk is based on the joint paper ({\it A.~Beltran, M.~Falla~Luza, D.~Marin, M.~Nicolau, Foliations and webs inducing Galois coverings, International Mathematics Research Notices, 12 (2016) 3768--3827}) and on current joint work with D.~Marin. A $k$-web is a geometric structure defined locally as the superposition of $k$ foliations. The image of a holomorphic foliation of degree $k$ on the complex projective space $\mathbb P^n$ by its Gauss map is a $k$-web. Motivated by previous work of Cerveau and Deserti, we introduce the notion of Galois holomorphic foliations on $\mathbb P^n$ as those whose Gauss map is a Galois covering when restricted to an appropriate Zariski open subset. This definition can be extended in a natural way to the notion of Galois k-webs defined on arbitrary projective manifolds. We characterize Galois foliations on $\mathbb P^2$ in terms of geometric data: their inflection divisor and their singularities. In particular we show that the classification of homogeneous Galois foliations corresponds to Klein's classification of ramified coverings of the projective line $\mathbb P^1$. We also determine the homogeneous Galois foliations on $\mathbb P^2$ that are flat. |