Projective normality of finite group quotients
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- by S. S. Kannan, S. K. Pattanayak and Pranab Sardar PDF
- Proc. Amer. Math. Soc. 137 (2009), 863-867 Request permission
Abstract:
In this paper, we prove that for any finite dimensional vector space $V$ over an algebraically closed field $k$, and for any finite subgroup $G$ of $GL(V)$ which is either solvable or is generated by pseudo reflections such that $|G|$ is a unit in $k$, the projective variety $\mathbb P(V)/G$ is projectively normal with respect to the descent of $\mathcal O(1)^{\otimes |G|}$.References
- Claude Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 77 (1955), 778–782. MR 72877, DOI 10.2307/2372597
- P. Erdös, A. Ginzburg, and A. Ziv, A theorem in additive number theory, Bull. Res. Council, Israel, 10 F (1961), 41-43.
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- Richard Kane, Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, vol. 5, Springer-Verlag, New York, 2001. MR 1838580, DOI 10.1007/978-1-4757-3542-0
- Hanspeter Kraft, Peter Slodowy, and Tonny A. Springer (eds.), Algebraische Transformationsgruppen und Invariantentheorie, DMV Seminar, vol. 13, Birkhäuser Verlag, Basel, 1989 (German). MR 1044582, DOI 10.1007/978-3-0348-7662-9
- D. Mumford, J. Fogarty, and F. Kirwan, Geometric invariant theory, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)], vol. 34, Springer-Verlag, Berlin, 1994. MR 1304906, DOI 10.1007/978-3-642-57916-5
- P. E. Newstead, Introduction to moduli problems and orbit spaces, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 51, Tata Institute of Fundamental Research, Bombay; Narosa Publishing House, New Delhi, 1978. MR 546290
- Emmy Noether, Der Endlichkeitssatz der Invarianten endlicher Gruppen, Math. Ann. 77 (1915), no. 1, 89–92 (German). MR 1511848, DOI 10.1007/BF01456821
- E. Noether, Der Endlichkeitssatz der Invarianten endlich linearer Gruppen der Charakteristik $p$, Nachr. Akad. Wiss. Gottingen (1926), 28-35.
- J-P. Serre, Groupes finis d’automorphismes d’anneaux locaux réguliers, Colloq. d’Alg. École Norm. de Jeunes Filles, Paris (1967), 1-11.
- G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canad. J. Math. 6 (1954), 274–304. MR 59914, DOI 10.4153/cjm-1954-028-3
Additional Information
- S. S. Kannan
- Affiliation: Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Padur Post Office, Siruseri, Tamilnadu, 603103, India
- Email: kannan@cmi.ac.in
- S. K. Pattanayak
- Affiliation: Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Padur Post Office, Siruseri, Tamilnadu, 603103, India
- Email: santosh@cmi.ac.in
- Pranab Sardar
- Affiliation: Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Padur Post Office, Siruseri, Tamilnadu, 603103, India
- MR Author ID: 854800
- Email: pranab@cmi.ac.in
- Received by editor(s): July 5, 2007
- Received by editor(s) in revised form: March 4, 2008
- Published electronically: September 15, 2008
- Communicated by: Ted Chinburg
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 863-867
- MSC (2000): Primary 14Lxx
- DOI: https://doi.org/10.1090/S0002-9939-08-09613-5
- MathSciNet review: 2457424