Normality and non-normality of group compactifications in simple projective spaces

Paolo Bravi[1]; Jacopo Gandini[1]; Andrea Maffei[1]; Alessandro Ruzzi[1]

  • [1] Dip.to di Matematica Università di Roma “La Sapienza” P.le A. Moro, 5 00185 ROMA ITALY

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 6, page 2435-2461
  • ISSN: 0373-0956

Abstract

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Given an irreducible representation V of a complex simply connected semisimple algebraic group G we consider the closure X of the image of G in ℙ ( End ( V ) ) . We determine for which V the variety X is normal and for which V is smooth.

How to cite

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Bravi, Paolo, et al. "Normality and non-normality of group compactifications in simple projective spaces." Annales de l’institut Fourier 61.6 (2011): 2435-2461. <http://eudml.org/doc/219727>.

@article{Bravi2011,
abstract = {Given an irreducible representation $V$ of a complex simply connected semisimple algebraic group $G$ we consider the closure $X$ of the image of $G$ in $\mathbb\{P\}(\text\{End\}(V))$. We determine for which $V$ the variety $X$ is normal and for which $V$ is smooth.},
affiliation = {Dip.to di Matematica Università di Roma “La Sapienza” P.le A. Moro, 5 00185 ROMA ITALY; Dip.to di Matematica Università di Roma “La Sapienza” P.le A. Moro, 5 00185 ROMA ITALY; Dip.to di Matematica Università di Roma “La Sapienza” P.le A. Moro, 5 00185 ROMA ITALY; Dip.to di Matematica Università di Roma “La Sapienza” P.le A. Moro, 5 00185 ROMA ITALY},
author = {Bravi, Paolo, Gandini, Jacopo, Maffei, Andrea, Ruzzi, Alessandro},
journal = {Annales de l’institut Fourier},
keywords = {semisimple algebraic groups; group compactifications; projective representations; wonderful varieties; symmetric spaces},
language = {eng},
number = {6},
pages = {2435-2461},
publisher = {Association des Annales de l’institut Fourier},
title = {Normality and non-normality of group compactifications in simple projective spaces},
url = {http://eudml.org/doc/219727},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Bravi, Paolo
AU - Gandini, Jacopo
AU - Maffei, Andrea
AU - Ruzzi, Alessandro
TI - Normality and non-normality of group compactifications in simple projective spaces
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 6
SP - 2435
EP - 2461
AB - Given an irreducible representation $V$ of a complex simply connected semisimple algebraic group $G$ we consider the closure $X$ of the image of $G$ in $\mathbb{P}(\text{End}(V))$. We determine for which $V$ the variety $X$ is normal and for which $V$ is smooth.
LA - eng
KW - semisimple algebraic groups; group compactifications; projective representations; wonderful varieties; symmetric spaces
UR - http://eudml.org/doc/219727
ER -

References

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  9. F. Knop, H. Kraft, D. Luna, T. Vust, Local properties of algebraic group actions, DMV Sem. 13 (1989), 63-75 Zbl0722.14032MR1044585
  10. A. Ruzzi, Smooth projective symmetric varieties with Picard number equal to one Zbl1213.14092
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  12. D.A. Timashev, Equivariant compactifications of reductive groups, Sb. Math. 194 (2003), 589-616 Zbl1074.14043MR1992080
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