Let $G$ be a complex, linear algebraic group and $H\subseteq G$ a closed **and normal** subgroup. Then, the quotient $G/H$ has the structure of a affine variety. I am looking for the most "modern" reference in English language for this statement. I would prefer a graduate level textbook most. Anything I find, however, restricts to the reductive case, which is not general enough for me.



Quotient of an algebraic group by a closed algebraic subgroup
You can prove that $G/H$ is quasi-projective, and a reference is Theorem 4.4.1 of Algebraic Quotients, Torus Actions, and Cohomology by A. Bialynicki-Birula, ‎J. Carrell, ‎and W.M. McGovern.


