Explicit birational models of marked elliptic surfaces of relative degree two

Abstract

We introduce explicit construction methods for two distinct birational models of elliptic surfaces equipped with a bisection --- or, more generally, a relative polarisation of degree two --- and double fibres. For Halphen surfaces of index two and Enriques surfaces, we illustrate how these give simple descriptions inside a toric variety.

36 pages, 2 figures, 5 tables. Comments are welcome!