An anti- affine group $G$ is defined to be an algebraic group with no global sections. Examples include abelian varieties and non trivial extensions of abelian varieties by torus (in characteristic $\neq$ 0 these are the only ones). What are the examples of such groups in characteristic 0, is there an 'obvious way' of constructing these? Any reference will be appreciated.


References


[1] Some structure theorems for algebraic groups, Michel Brion.



A non trivial example of an anti -affine algebraic group
Brion's paper [Anti-affine algebraic groups](https://arxiv.org/abs/0710.5211) gives the complete classification over fields whose closure is separable. The examples are not very easy to describe.


