Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups

Jean-Marc Drézet[1]; Günther Trautmann[2]

  • [1] Institut de Mathématiques, UMR 7586 du CNRS, Aile 45-55, 5ème étage, 2 place Jussieu, 75251 Paris Cedex 05 (France)
  • [2] Universität Kaiserslautern, Fachbereich Mathematik, Erwin-Schrödinger Strasse, 67663 Kaiserslautern (Allemagne)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 1, page 107-192
  • ISSN: 0373-0956

Abstract

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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 Aut ( E ) × Aut ( F ) 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.

How to cite

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Drézet, Jean-Marc, and Trautmann, Günther. "Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups." Annales de l’institut Fourier 53.1 (2003): 107-192. <http://eudml.org/doc/116032>.

@article{Drézet2003,
abstract = {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 $\{\rm Aut\}(E)\times \{\rm Aut\}(F)$ 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.},
affiliation = {Institut de Mathématiques, UMR 7586 du CNRS, Aile 45-55, 5ème étage, 2 place Jussieu, 75251 Paris Cedex 05 (France); Universität Kaiserslautern, Fachbereich Mathematik, Erwin-Schrödinger Strasse, 67663 Kaiserslautern (Allemagne)},
author = {Drézet, Jean-Marc, Trautmann, Günther},
journal = {Annales de l’institut Fourier},
keywords = {algebraic quotients; good quotients; non-reductive groups; moduli spaces; geometric invariant theory; actions on coherent sheaves; polarization; geometric quotient},
language = {eng},
number = {1},
pages = {107-192},
publisher = {Association des Annales de l'Institut Fourier},
title = {Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups},
url = {http://eudml.org/doc/116032},
volume = {53},
year = {2003},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 1
SP - 107
EP - 192
AB - 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 ${\rm Aut}(E)\times {\rm Aut}(F)$ 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.
LA - eng
KW - algebraic quotients; good quotients; non-reductive groups; moduli spaces; geometric invariant theory; actions on coherent sheaves; polarization; geometric quotient
UR - http://eudml.org/doc/116032
ER -

References

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