Bounding the regularity of subschemes invariant under Pfaff fields on projective spaces
Joana D. A. CruzUniversidade Federal de Juiz de Fora, Brazil
Eduardo EstevesInstituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
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.
Cite this article
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