Resumen de A sharp lower bound for the canonical volume of 3-folds of general type

Meng Chen

• Let V be a smooth projective 3-fold of general type. Denote by K 3, a rational number, the self-intersection of the canonical sheaf of any minimal model of V. One defines K 3 as the canonical volume of V. Assume p g (V) = 2. We show that , which is a sharp lower bound. Then we classify those V with small volume. We also give some new examples with p g = 2 which have maximal canonical stability index. Finally, we give an application to 4-folds of general type.

  The author is supported by the National Natural ScienceFoundation of China.