A finiteness theorem for elliptic Calabi-Yau threefolds

Calabi-Yau varieties are generalizations of elliptic curves and K3 surfaces. From the point of view of algebraic geometry, the question of boundedness of such varieties seems interesting. Following the work of Mark Gross, we prove that up to birational equivalence there are only finitely many families of 3-dimensional Calabi-Yau varieties that satisfy certain conditions. More precisely, singularities should be terminal and factorial, and the given variety should admit a fibration into elliptic curves over a rational surface.