2003/04/11 by Eduardo Esteves, E. Esteves, Steven L. Kleiman +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Numerical methods for differential equations #Quantum chaos and dynamical systems #math.AG #math.DS #msc:14B05 #msc:14F10 #msc:14H99 #msc:32S65 #msc:37F75
paper · pdf · doi:10.48550/arxiv.math/0304148
18 pages; AMSLaTeX
arxiv created 2003/04/11 · arxiv updated 2009/11/30
Let ωbe a Pfaff system of differential forms on a projective space. Let S be its singular locus, and Y a solution of ω=0. We prove Y∩ S is of codimension at most 1 in Y, just as Jouanolou suspected; he proved this result assuming ωis completely integrable, and asked if the integrability is, in fact, needed. Furthermore, we prove a lower bound on the Castelnuovo--Mumford regularity of Y∩ S. As in two related articles, we derive upper bounds on numerical invariants of Y, thus contributing to the solution of the Poincare problem. We work with Pfaff fields not necessarily induced by Pfaff systems, with ambient spaces more general than projective spaces, and usually in arbitrary characteristic.