Standard model of degree 1 del Pezzo fibrations

We discuss the construction of some good birational models for three-dimensional del Pezzo fibrations over a curve. These fibrations (along with conic bundles and Fano varieties) occur when the Minimal Model Program is applied to a three-dimensional rationally connected variety. It is natural to ask if one can obtain a model whose canonical divisor is Cartier (a Gorenstein model), and with as good singularities as possible. We explain how to construct Gorenstein model with canonical singularities for a degree 1 del Pezzo fibrations that admit an action of a finite group $G$.