Distribuições de codimensão 1 e primeira classe de Chern nula em variedades Fano tridimensionais

Abstract

The study of holomorphic distributions and foliations through the properties of their singular scheme and tangent sheaf allows for the classification and description of their corresponding moduli spaces. This approach can be seen, for example, in the works of O. Calvo Andrade, M. Corrêa, and M. Jardim [5], or H. Galeano, M. Jardim, and A. Muniz [12]. The main objective of this work is to establish a classification of codimensionone distributions on X, a smooth three-dimensional Fano variety with Picard number 1, whose tangent sheaf is locally free and has a vanishing first Chern class. This classification will be carried out by describing the tangent sheaf and the singular scheme of the distributions, analyzing case by case within the Iskovskikh and Mukai classification of three-dimensional Fano varieties [16], [17], [22].