A combinatorial construction of sets with good quotients by an action of a reductive group
Volume 87 / 2001
Colloquium Mathematicum 87 (2001), 85-102
MSC: Primary 14L24, 14L30.
DOI: 10.4064/cm87-1-5
Abstract
The aim of this paper is to construct open sets with good quotients by an action of a reductive group starting with a given family of sets with good quotients. In particular, in the case of a smooth projective variety $X$ with $\mathop {\rm Pic}\nolimits (X)= {\cal Z}$, we show that all open sets with good quotients that embed in a toric variety can be obtained from the family of open sets with projective good quotients. Our method applies in particular to the case of Grassmannians.
