Hurwitz complete sets of factorizations in the modular group and the classification of Lefschetz elliptc fibrations over the disk

Abstract

Given any matrix B in SL(2,Z), we will describe an algorithm that provides at least one elliptic fibration over the disk, relatively minimal and Lefschetz, within each topological equivalence class, whose total monodromy is the conjugacy class of B.

arXiv comment15 pages