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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 Pic(X) = 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.
Joanna Święcicka. "A combinatorial construction of sets with good quotients by an action of a reductive group." Colloquium Mathematicae 87.1 (2001): 85-102. <http://eudml.org/doc/283830>.
@article{JoannaŚwięcicka2001, 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 Pic(X) = 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.}, author = {Joanna Święcicka}, journal = {Colloquium Mathematicae}, keywords = {group actions; orbit spaces; good quotients}, language = {eng}, number = {1}, pages = {85-102}, title = {A combinatorial construction of sets with good quotients by an action of a reductive group}, url = {http://eudml.org/doc/283830}, volume = {87}, year = {2001}, }
TY - JOUR AU - Joanna Święcicka TI - A combinatorial construction of sets with good quotients by an action of a reductive group JO - Colloquium Mathematicae PY - 2001 VL - 87 IS - 1 SP - 85 EP - 102 AB - 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 Pic(X) = 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. LA - eng KW - group actions; orbit spaces; good quotients UR - http://eudml.org/doc/283830 ER -