Catriona MacLean: Explicit Noether-Lefschetz for arbitrary threefolds.

Abstract: The traditional Noether-Lefschetz theorem states that in degree at least 4 a generic surface in the projective space P3 has no curves other than complete intersections with other surfaces in P3. Generic in this sense means outside of a countable union of sub-varieties. The explicit Noether-Lefschetz theorem is a refinement due to Voisin and Green independently stating that for surfaces of degree d each of these "bad" subvarieties is of codimension at least d-3. We will show how to extend this work to threefolds other than P3.