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.