The combinatorial type of an elliptic surface with a zero section is the pair of the -type of the singular fibers and the torsion part of the Mordell–Weil group. We determine the set of connected components of the moduli of elliptic surfaces with fixed combinatorial type. Our method relies on the theory of Miranda and Morrison on the structure of a genus of even indefinite lattices and on computer-aided calculations of -adic quadratic forms.
"Connected Components of the Moduli of Elliptic Surfaces." Michigan Math. J. 67 (3) 511 - 559, August 2018. https://doi.org/10.1307/mmj/1528941621