Local properties of algebraic group actions

Knop F, Kraft H, Luna D, Vust T (1989)

Publication Language: English

Publication Type: Book chapter / Article in edited volumes

Publication year: 1989

Publisher: Birkhäuser Verlag

Edited Volumes: Algebraische Transformationsgruppen und Invariantentheorie

City/Town: Basel-Boston

Book Volume: 13

Pages Range: 63-76


Let G be a connected linear algebraic group acting on a normal variety X. This note contains two proofs of a basic theorem of Sumihiro which we hope are more transparent than the original one.

Theorem: 1. Every point of X has a G-stable open quasi-projective neighborhood.
2. If X is quasi-projective then it can be equivariantly embedded into a projective space.

The first proof uses the language of line bundles, the second field and valuation theory. In the last section, the Picard group of G is studied.

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How to cite


Knop, F., Kraft, H., Luna, D., & Vust, T. (1989). Local properties of algebraic group actions. In H. Kraft, P. Slodowy, T. Springer (Eds.), Algebraische Transformationsgruppen und Invariantentheorie. (pp. 63-76). Basel-Boston: Birkhäuser Verlag.


Knop, Friedrich, et al. "Local properties of algebraic group actions." Algebraische Transformationsgruppen und Invariantentheorie. Ed. H. Kraft, P. Slodowy, T. Springer, Basel-Boston: Birkhäuser Verlag, 1989. 63-76.

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