448 research outputs found
Codimension one Fano distributions on Fano manifolds
In this paper we investigate codimension one Fano distributions on Fano
manifolds with Picard number one. We classify Fano distributions of maximal
index on complete intersections in weighted projective spaces, Fano contact
manifolds, Grassmannians of lines and their linear sections, and describe their
moduli spaces. As a consequence, we obtain a classification of codimension one
del Pezzo distributions on Fano manifolds with Picard number one.Comment: 23 page
Darboux–Jouanolou–Ghys integrability for one-dimensional foliations on toric varieties
AbstractWe use the existence of homogeneous coordinates for simplicial toric varieties to prove a result analogous to the Darboux–Jouanolou–Ghys integrability theorem for the existence of rational first integrals for one-dimensional foliations
On the Singular Scheme of Split Foliations
We prove that the tangent sheaf of a codimension one locally free
distribution splits as a sum of line bundles if and only if its singular scheme
is arithmetically Cohen-Macaulay. In addition, we show that a foliation by
curves is given by an intersection of generically transversal holomorphic
distributions of codimension one if and only if its singular scheme is
arithmetically Buchsbaum. Finally, we establish that these foliations are
determined by their singular schemes, and deduce that the Hilbert scheme of
certain arithmetically Buchsbaum schemes of codimension is birational to a
Grassmannian.Comment: 21 page
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