Abstract

In this paper we study del Pezzo fibrations z:X→ℙ1 of degree 1 and 2 such that X is smooth, rk Pic(X)=2 and Open image in new window These are examples of smooth birationally rigid 3-fold Mori fibre spaces. We describe all birational transformations of the 3-fold X into elliptic fibrations, fibrations of surfaces of Kodaira dimension zero, and canonical Fano 3-folds.

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