Good quotients of Mori dream spaces

Good quotients of Mori dream spaces
HTML articles powered by AMS MathViewer

by Hendrik Bäker PDF

Proc. Amer. Math. Soc. 139 (2011), 3135-3139 Request permission

We show that good quotients of algebraic varieties with finitely generated Cox ring have again finitely generated Cox ring.

References

Michela Artebani, Jürgen Hausen, and Antonio Laface, On Cox rings of K3 surfaces, Compos. Math. 146 (2010), no. 4, 964–998. MR 2660680, DOI 10.1112/S0010437X09004576
Ivan V. Arzhantsev, Affine embeddings of homogeneous spaces, Surveys in geometry and number theory: reports on contemporary Russian mathematics, London Math. Soc. Lecture Note Ser., vol. 338, Cambridge Univ. Press, Cambridge, 2007, pp. 1–51. MR 2306139, DOI 10.1017/CBO9780511721472.002
Arzhantsev, Ivan V.; Derenthal, Ulrich; Hausen, Jürgen; Laface, Antonio: Cox rings. Preprint, arXiv:1003.4229v1.
Frank D. Grosshans, Algebraic homogeneous spaces and invariant theory, Lecture Notes in Mathematics, vol. 1673, Springer-Verlag, Berlin, 1997. MR 1489234, DOI 10.1007/BFb0093525
Jürgen Hausen, Geometric invariant theory based on Weil divisors, Compos. Math. 140 (2004), no. 6, 1518–1536. MR 2098400, DOI 10.1112/S0010437X04000867
Yi Hu and Sean Keel, Mori dream spaces and GIT, Michigan Math. J. 48 (2000), 331–348. Dedicated to William Fulton on the occasion of his 60th birthday. MR 1786494, DOI 10.1307/mmj/1030132722
Friedrich Knop, Hanspeter Kraft, and Thierry Vust, The Picard group of a $G$-variety, Algebraische Transformationsgruppen und Invariantentheorie, DMV Sem., vol. 13, Birkhäuser, Basel, 1989, pp. 77–87. MR 1044586