20 sep 2023 -- 11:30
Aula Tricerri, DIMaI, Firenze
Seminari di Geometria del Dini
Abstract.
We study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of such foliations by curves up to degree 3, also describing the possible singular schemes. In particular, we prove that foliations by curves of degree 1 or 2 are either contained on a pencil of planes or legendrian, and are given by the complete intersection of two codimension one distributions. We prove that the conormal sheaf of a foliation by curves of degree 3 with reduced singular scheme either splits as a sum of line bundles or is an instanton bundle. We also describe their moduli spaces. This is Joint work with Marcos Jardim and Simone Marchesi.