This note is an extended version of a thirty minutes talk given at the "XIX
Congresso dell'Unione Matematica Italiana", held in Bologna from September 12th
to September 17th, 2011. This was essentially a survey talk about connections
between Kobayashi hyperbolicity properties and positivity properties of the
canonical bundle of projective algebraic varieties.Comment: 9 pages, no figures, to appear on Boll. Unione Mat. Ita
