Birational geometry and the canonical ring of a family of determinantal 3-folds

Abstract

Few explicit families of 3-folds are known for which the computation of the canonical ring is accessible and the birational geometry non-trivial. In this note we investigate a family of determinantal 3-folds in ${\mathbb{P}}^2\times {\mathbb{P}}^3$ where this is the case.

v2: final version