We prove that the bounded derived category of coherent sheaves on a smooth projective complex variety reconstructs the isomorphism classes of fibrations onto smooth projective curves of genus . Moreover, in dimension at most four, we prove that the same category reconstructs the isomorphism classes of fibrations onto normal projective surfaces with positive holomorphic Euler characteristic and admitting a finite morphism to an abelian variety. Finally, we study the derived invariance of a class of fibrations with minimal base dimension under the condition that all the Hodge numbers of type are derived invariant.
"Derived equivalence and fibrations over curves and surfaces." Kyoto J. Math. 62 (4) 683 - 706, December 2022. https://doi.org/10.1215/21562261-2022-0022