Regularity of subschemes invariant under Pfaff fields on projective spaces
Algebraic Geometry
2009-02-16 v1 Complex Variables
Dynamical Systems
Abstract
A Pfaff field on a projective space is a map from the sheaf of differential s-forms, for a certain s, to an invertible sheaf. The interesting ones are those arising from a Pfaff system, as they give rise to a distribution away from their singular locus. A subscheme of the projective space is said to be invariant under the Pfaff field, if the latter induces a Pfaff field on the subscheme. We give bounds for the Castelnuovo-Mumford regularity of invariant complete intersection subschemes (more generally, arithmetically Cohen-Macaulay subschemes) of dimension s, depending on how singular these schemes are, thus bounding the degrees of the hypersurfaces that cut them out.
Cite
@article{arxiv.0902.2322,
title = {Regularity of subschemes invariant under Pfaff fields on projective spaces},
author = {Joana D. A. S. Cruz and Eduardo Esteves},
journal= {arXiv preprint arXiv:0902.2322},
year = {2009}
}