Projective normality of G.I.T. quotient varieties modulo finite groups

We prove that for any finite dimensional representation V of a finite group G of order n the quotient variety G∖ℙ(V) is projectively normal with respect to descent of (1) ⊗l where l = lcm{1,2,3,4,...,n}. We also prove that for the tautological representation V of the alternating group A n the projec...

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Bibliographic Details
Published in:Communications in algebra 2017-07, Vol.45 (7), p.2996-3004
Main Authors: Goyal, Pallav, Pattanayak, S. K.
Format: Article
Language:English
Subjects:
Algebra
Bundling
Descent
G.I.T. Quotient
line bundle
Mathematical analysis
Normality
projective normality
Quotients
Representations
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Summary:We prove that for any finite dimensional representation V of a finite group G of order n the quotient variety G∖ℙ(V) is projectively normal with respect to descent of (1) ⊗l where l = lcm{1,2,3,4,...,n}. We also prove that for the tautological representation V of the alternating group A n the projective variety A n ∖ℙ(V) is projectively normal with respect to the descent of the above line bundle.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2016.1233334