Holomorphic symmetric differentials, abelian variesties, complex tori, and parallelizable compact complex manifods
Ernesto Mistretta
(U. Padova)



We review some recent constructions obtained with S. Urbinati on positivity, base loci, and Iitaka fibrations for higher rank vector bundles, then use some of these to obtain a biholomorphic and a bimeromorphic characterization of abelian varieties. Then we see how to extend some of these results to complex tori and to compact complex parallelizable manifolds.