Hypersurfaces in multiprojective spaces are defined by a multigraded polynomial. Despite their apparent simplicity, their birational geometry can be quite complicated. For example, they can have infinite birational automorphism groups. We give a complete picture of their birational geometry and compute their effective cones and nef cones. As an application, we give a negative answer to a question of Cascini and Gongyo.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/5285