On the singular scheme of split foliations Mauricio Correa Jr.Marcos JardimRenato Martins 32S6537F75Holomorphic foliationsreflexive sheavessplit vector bundles We prove that the tangent sheaf of a codimension-one locally free distribution splits as a sum of line bundles if and only if its singular scheme is arithmetically Cohen-Macaulay. In addition, we show that a foliation by curves is given by an intersection of generically transversal holomorphic distributions of codimension one if and only if its singular scheme is arithmetically Buchsbaum. Finally, we establish that these foliations are determined by their singular schemes, and deduce that the Hilbert scheme of certain arithmetically Buchsbaum schemes of codimension two is birational to a Grassmannian. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5672 10.1512/iumj.2015.64.5672 en Indiana Univ. Math. J. 64 (2015) 1359 - 1381 state-of-the-art mathematics http://iumj.org/access/