ON CALABI-YAU ELLIPTIC THREEFOLDS IN P^2-BUNDLES

The aim of the thesis is the study and the classification of the families of elliptic threefolds which are embedded as anticanonical divisors in some particular P^2-bundle over a surface. In particular, the case where the base surface is the projective plane is studied in depth. The main results of the thesis are: * a theorem on the structure of the non-Kodaira fibres in an elliptic threefold; * the finiteness of the number of families of smooth elliptic threefolds in the P^2-bundle P(L^a + L^b + O) over a surface, where O is the trivial bundle and L is an ample line bundle; * a phisical result concerning F-theory, on the tadpole cancellation and universal tadpole cancellation relations.