By the well-known Cartan-Grothendieck-Serreās result, the ampleness of a line bundle on a projective variety is characterized in terms of the vanishing of the higher cohomology groups. By weakening this condition, we obtain a notion of 'partial ampleness', that intuitively measures how much a line bundle is far from being ample and that shares many important properties with the usual one. In the first part of this talk, I will give an introduction to the theory of partially ample line bundles and discuss some of their main features. In the second part of the talk, I will present some original results that help us to interpret geometrically the partial ampleness of a line bundle. |

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