Distribuições de codimensão 1 no espaço projetivo tridimensional

Abstract

In this work, we present recent results by Omegar, Corrêa and M. Jardim that classify distributions on the three-dimensional projective space on codimensions zero or one. For the last case, these authors have shown that the tangent bundle is stable whenever it does not split as a sum of line bundles. For those results, some algebraic geometric invariants like Chern classes are necessary. Hence, we will briefly introduce the Theory of algebraic varieties, schemes and sheaves over them. In particular, some notions regarding reflexive sheaves present in [8] will be shown. Moreover, we present some results concerning the Moduli spaces of distributions that are part of the same work, in terms of the Grothendieck’s Quot-Scheme for the tangent bundle. Such spaces will be carefully constructed following the approach in [9], where these are seen as a generalization of Grassmann varieties.