Determinantal criteria for transversality of morphisms

Dan Laksov and Robert Speiser

Vol. 156 (1992), No. 2, 307–328

DOI: 10.2140/pjm.1992.156.307

Abstract

When is a sufficiently general member f_t : X_t → Y , of a family of maps of smooth schemes, transverse to a given map from a smooth scheme Z to Y ? Here we give criteria valid over any universally catenary base scheme in any characteristic. Roughly speaking, our criteria will hold whenever the subscheme where an appropriate bundle map drops rank is determinantal, in the sense that it has the smallest possible dimension.

Mathematical Subject Classification 2000

Primary: 14M12

Secondary: 14A15

Milestones

Received: 11 March 1991

Published: 1 December 1992