Counting curves which move with threefolds

Abstract

Let X be a (possibly nodal) K-trivial threefold moving in a fixed ambient space P. Suppose X contains a continuous family of curves, all of whose members satisfy certain unobstructedness conditions in P. A formula is given for computing the corresponding virtual number of curves, that is, the number of curves on a generic deformation of X "contributed by" the continuous family on X.

25 pages, LaTeX2e. Several minor corrections and clairifications; theorem 3.3. slighlty strengthened; references updated