A Pfaff field on is a map from the sheaf of differential -forms 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 is said to be invariant under if induces a Pfaff field . We give bounds for the Castelnuovo–Mumford regularity of invariant complete intersection subschemes (more generally, arithmetically Cohen–Macaulay subschemes) of dimension , depending on how singular these schemes are, thus bounding the degrees of the hypersurfaces that cut them out.
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Joana D. A. Cruz, Eduardo Esteves, Bounding the regularity of subschemes invariant under Pfaff fields on projective spaces. Comment. Math. Helv. 86 (2011), no. 4, pp. 947–965DOI 10.4171/CMH/244