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

Bravi, Paolo; Gandini, Jacopo; Maffei, Andrea; Ruzzi, Alessandro

doi:10.5802/aif.2679

Normality and non-normality of group compactifications in simple projective spaces
[Normalité et non-normalité des plongements d’un groupe dans un espace projectif simple]

Bravi, Paolo ¹ ; Gandini, Jacopo ¹ ; Maffei, Andrea ¹ ; Ruzzi, Alessandro ¹

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

Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2435-2461.

Résumé
Abstract

Étant donné une représentation irreductible $V$ d’un groupe complexe semi-simple et simplement connexe $G$ , nous considérons l’adhérence $X$ de l’image de $G$ dans $ℙ (End (V))$ . Nous déterminons les représentations $V$ pour lesquelles $X$ est normale, respectivement lisse.

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.

MR | 1 citation dans Numdam

DOI : 10.5802/aif.2679

Classification : 14L30, 14M17
Keywords: semisimple algebraic groups, group compactifications
Mot clés : groupes algébriques semi-simples, plongements projectifs d’un groupe

Affiliations des auteurs :

Bravi, Paolo ¹ ; Gandini, Jacopo ¹ ; Maffei, Andrea ¹ ; Ruzzi, Alessandro ¹

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

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     title = {Normality and non-normality of group compactifications in simple projective spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {2435--2461},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {61},
     number = {6},
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     doi = {10.5802/aif.2679},
     mrnumber = {2976317},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2679/}
}

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Bravi, Paolo; Gandini, Jacopo; Maffei, Andrea; Ruzzi, Alessandro. Normality and non-normality of group compactifications in simple projective spaces. Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2435-2461. doi : 10.5802/aif.2679. http://www.numdam.org/articles/10.5802/aif.2679/

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