Mihnea Popa,
Global generation and normal generation on abelian varieties
The main purpose of this talk is to report on some highly interesting
recent work of Giuseppe Pareschi on vector bundles on abelian
varieties. Concretely I would like to present some cohomological
criteria for global generation and normal generation (the higher rank
analogue of projective normality) of vector bundles, the main ingredient
involved being the notion of "skew-Potryagin" product. Using these
results, Pareschi has been able to prove a conjecture of Rob Lazarsfeld
on syzygies of abelian varieties. If time permits, I will also very
briefly mention some applications to linear series on moduli spaces of
vector bundles on curves.