[Variétés de modules de morphismes décomposables de faisceaux et quotients par des groupes non-réductifs]
Nous étendons les méthodes utilisées en géométrie invariante à l’étude de l’action de sur étant des faisceaux cohérents décomposables, dont les groupes d’automorphismes ne sont pas nécessairement réductifs. Étant donné une linéarisation de cette action, un homomorphisme est dit stable si son orbite relativement au radical unipotent de est contenue dans le lieu stable relativement à l’action du sous-groupe réductif naturel de . Nous donnons des conditions numériques effectives portant sur la linéarisation pour que l’ouvert correspondant des points semi-stables admette un bon quotient au sens de la géométrie invariante, qui soit projectif, et pour que ce quotient restreint à l’ouvert des homomorphismes stables soit un quotient géométrique.
We extend the methods of geometric invariant theory to actions of non–reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non–reductive. Given a linearization of the natural action of the group on Hom(E,F), a homomorphism is called stable if its orbit with respect to the unipotent radical is contained in the stable locus with respect to the natural reductive subgroup of the automorphism group. We encounter effective numerical conditions for a linearization such that the corresponding open set of semi- stable homomorphisms admits a good and projective quotient in the sense of geometric invariant theory, and that this quotient is in addition a geometric quotient on the set of stable homomorphisms.
Classification : 14L30, 14D20
Mots clés : quotients algébriques, bons quotients, groupes non-réductifs, variétés de modules
@article{AIF_2003__53_1_107_0,
author = {Dr\'ezet, Jean-Marc and Trautmann, G\"unther},
title = {Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups},
journal = {Annales de l'Institut Fourier},
pages = {107--192},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {53},
number = {1},
year = {2003},
doi = {10.5802/aif.1941},
zbl = {1034.14023},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1941/}
}
TY - JOUR AU - Drézet, Jean-Marc AU - Trautmann, Günther TI - Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups JO - Annales de l'Institut Fourier PY - 2003 DA - 2003/// SP - 107 EP - 192 VL - 53 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1941/ UR - https://zbmath.org/?q=an%3A1034.14023 UR - https://doi.org/10.5802/aif.1941 DO - 10.5802/aif.1941 LA - en ID - AIF_2003__53_1_107_0 ER -
Drézet, Jean-Marc; Trautmann, Günther. Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups. Annales de l'Institut Fourier, Tome 53 (2003) no. 1, pp. 107-192. doi : 10.5802/aif.1941. https://aif.centre-mersenne.org/articles/10.5802/aif.1941/
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