Title:
About some work of Van de Ven 

Abstract:
This talk is a try out of a talk I’ll give in Leiden for a general math. audience.

I explain 2 important aspects of van de Ven’s work: firstly, (holomorphic) vector bundles, and, secondly, the topology of four manifolds.

The first aspect will be illustrated with a theorem which implies a special case of Hartshorne’s conjecture about complete intersections in projective space. For the second I look at connected sums of projective planes and ask when these can have an almost complex structure and if so when do these come from a true complex structure. Here there is a (somewhat hidden) relation with holomorphic vector bundles.