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

• 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 recutive. Given a linearization of the natural actionof the group Aut(E)xAut(F) on Hom(E,F), a homomorphism iscalled stable if its orbit with respect to the unipotentradical is contained in the stable locus with respect to thenatural reductive subgroup of the automorphism group. Weencounter effective numerical conditions for a linearizationsuch that the corresponding open set of semi-stable homomorphismsadmits a good and projective quotient in the sense of geometricinvariant theory, and that this quotient is in additiona geometric quotient on the set of stable homomorphisms.

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Author: Jean Marc Drezed, Günther Trautmann urn:nbn:de:hbz:386-kluedo-7964 Preprints (rote Reihe) des Fachbereich Mathematik (301) Preprint English 1996 1996 Technische Universität Kaiserslautern 2000/04/03 algebraic geometry ; invariant theory; moduli spaces Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 14-XX ALGEBRAIC GEOMETRY / 14Dxx Families, fibrations / 14D20 Algebraic moduli problems, moduli of vector bundles (For analytic moduli problems, see 32G13) 14-XX ALGEBRAIC GEOMETRY / 14Lxx Algebraic groups (For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45) / 14L30 Group actions on varieties or schemes (quotients) [See also 13A50, 14L24] Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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