Very ample linear systems on abelian varieties

The first author is partially supported by N.S.F. grant DMS 92-03919 and the European Science Project Geometry of Algebraic Varieties, contract no. SCI-0398-C (A)     

Monads and moduli of vector bundles

Horrocks has shown that every vector bundle on ₂ and ₃ admits a certain double-ended resolution by line bundles, which he called a monad. We reprove Horrocks' results taking much care of uniqueness of the monads so obtained. This technique should be useful for constructing moduli spaces of stable vector bundles.     

Intersection Theory of Toroidal Compactifications of A4

We determine the intersection theory on the Igusa compactificationand the second Voronoi compactification of A₄. 2000 MathematicsSubject Classification 14K10.     

The <Emphasis Type="Italic">L</Emphasis>-series of a cubic fourfold

We study the L-series of cubic fourfolds. Our main result is that, if X/C is a special cubic fourfold associated to some polarized K3 surface S, defined over a number field K and satisfying , then X has a model over K such that the L-series of the primitive cohomology of X/K can be expressed in terms of the L-series of S/K. This allows us to compute the L-series for a discrete dense subset of cubic fourfolds in the moduli spaces of certain special cubic fourfolds. We also discuss a concrete example.