Regularity of subschemes invariant under Pfaff fields on projective spaces

Joana D. A. S. Cruz; Eduardo Esteves

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arXiv · 0902.2322

Regularity of subschemes invariant under Pfaff fields on projective spaces

Joana D. A. S. Cruz·Eduardo Esteves

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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.

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BibTeX RIS

Joana D. A. S. Cruz, Eduardo Esteves. 2009-02-13. Regularity of subschemes invariant under Pfaff fields on projective spaces. https://arxiv.org/abs/0902.2322

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