Enumeration and normal forms of singularities in Cauchy-Riemann structures.

摘要

The objects of study are real m-submanifolds M of complex n-manifolds. The goal is to describe the topological and complex-analytic behavior of submanifolds with complex tangents--points where the tangent space and its rotation by the complex structure operator do not meet transversely.; Complex tangents of M form a degeneracy locus of a bundle map over M. When the immersion of M is generic with respect to a transversality condition on the Gauss map, a construction of Thom and Porteous is used in a theorem relating the fundamental class of the locus to chern and pontrjagin classes. Recent theorems of Fulton and Pragacz are applied to describe other global complex tangency phenomena.; The local geometry near a complex tangent is considered in the {dollar}m