Geodesic
Framed moduli spaces and tuples of operators
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 5, pp. 187-209 
S. N. Fedotov. Framed moduli spaces and tuples of operators. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 5, pp. 187-209. http://geodesic.mathdoc.fr/item/FPM_2012_17_5_a12/
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     author = {S. N. Fedotov},
     title = {Framed moduli spaces and tuples of operators},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {187--209},
     year = {2012},
     volume = {17},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_5_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this work, we address the classical problem of classifying tuples of linear operators and linear functions on a finite-dimensional vector space up to base change. Having adopted for the situation considered a construction of framed moduli spaces of quivers, we develop an explicit classification of tuples belonging to a Zariski open subset. For such tuples we provide a finite family of normal forms and a procedure allowing one to determine whether two tuples are equivalent.

[1] Kokorin A. I., Martyanov V. I., “Universalnye rasshirennye teorii”, Algebra, Irkutsk, 1973, 107–113 | MR

[2] Popov V. L., “Dve orbity: kogda odna lezhit v zamykanii drugoi?”, Tr. MIRAN im. V. A. Steklova, 264, 2009, 152–164 | MR

[3] Baur W., “Decidability and undecidability of theories of Abelian groups with predicates for subgroups”, Compositio Math., 31 (1975), 23–30 | MR | Zbl

[4] Engel J., Reineke M., “Smooth models of quiver moduli”, Math. Z., 262 (2009), 817–848 | DOI | MR | Zbl

[5] Fedotov S., “Framed moduli and Grassmannians of submodules”, Trans. Amer. Math. Soc. (to appear) , arXiv: 1010.4761v2 | MR

[6] Huisgen-Zimmermann B., “Classifying representations by way of Grassmannians”, Trans. Amer. Math. Soc., 359 (2007), 2687–2719 | DOI | MR | Zbl

[7] King A. D., “Moduli of representations of finite-dimensional algebras”, Quart. J. Math. Oxford Ser. (2), 45:180 (1994), 515–530 | DOI | MR | Zbl

[8] Mumford D., Fogarty J., Kirwan F., Geometric Invariant Theory, Ergebnisse Math. ihrer Grenzgebiete (2), Springer, Berlin, 1994 | DOI | MR | Zbl

[9] Reineke M., “Framed quiver moduli, cohomology, and quantum groups”, J. Algebra, 320:1 (2008), 94–115 | DOI | MR | Zbl