Kyoto Journal of Mathematics

On a smooth compactification of PSL(n,C)/T

Indranil Biswas, S. Senthamarai Kannan, and D. S. Nagaraj

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Abstract

Let T be a maximal torus of PSL(n,C). For n4, we construct a smooth compactification of PSL(n,C)/T as a geometric invariant theoretic quotient of the wonderful compactification PSL(n,C)¯ for a suitable choice of T-linearized ample line bundle on PSL(n,C)¯. We also prove that the connected component, containing the identity element, of the automorphism group of this compactification of PSL(n,C)/T is PSL(n,C) itself.

Article information

Source
Kyoto J. Math., Volume 56, Number 1 (2016), 165-175.

Dates
Received: 26 August 2012
Revised: 16 January 2015
Accepted: 16 January 2015
First available in Project Euclid: 15 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1458047881

Digital Object Identifier
doi:10.1215/21562261-3445183

Mathematical Reviews number (MathSciNet)
MR3479321

Zentralblatt MATH identifier
1334.14030

Subjects
Primary: 14F17: Vanishing theorems [See also 32L20]

Keywords
Wonderful compactification GIT quotients automorphism group Frobenius splitting

Citation

Biswas, Indranil; Kannan, S. Senthamarai; Nagaraj, D. S. On a smooth compactification of $\operatorname{PSL}(n,\mathbb{C})/T$. Kyoto J. Math. 56 (2016), no. 1, 165--175. doi:10.1215/21562261-3445183. https://projecteuclid.org/euclid.kjm/1458047881


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