Monodromy groups of regular elliptic surfaces (Q1601777)

Monodromy in analytic families of smooth complex surfaces yields groups of isotopy classes of orientation preserving diffeomorphisms for each family member \(X\). In this paper the author constructs families of regular elliptic surfaces with positive geometric genus, for each possible deformation type. Studying the monodromy of these families he can prove the main result of this paper: Theorem. Let \(X\) be a minimal elliptic surface with positive geometric genus \(p_g\) and vanishing irregularity \(q\), then there exist families of elliptic surfaces containing \(X\), such that the induced monodromy actions on the homology lattice \(L_X:=H_2/\)torsion generate the group of isometries of real spinor norm one fixing the canonical class.