We show that a homomorphism of algebras is a categorical epimorphism if and only if all induced morphisms of the associated module varieties are immersions. This enables us to classify all minimal singularities in the subvarieties of modules from homogeneous standard tubes.
@article{bwmeta1.element.bwnjournal-article-cmv82i2p287bwm,
author = {Grzegorz Zwara},
title = {Immersions of module varieties},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {287-299},
zbl = {1005.16011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv82i2p287bwm}
}
Zwara, Grzegorz. Immersions of module varieties. Colloquium Mathematicae, Tome 79 (1999) pp. 287-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv82i2p287bwm/
[000] [1] S. Abeasis, A. Del Fra and H. Kraft, The geometry of representations of , Math. Ann. 256 (1981), 401-418. | Zbl 0477.14027
[001] [2] V. I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (1971), 29-43.
[002] [3] M. Auslander, I. Reiten and S. O. Smalο, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, 1995.
[003] [4] K. Bongartz, A geometric version of the Morita equivalence, J. Algebra 139 (1991), 159-171. | Zbl 0787.16011
[004] [5] K. Bongartz, Minimal singularities for representations of Dynkin quivers, Comment. Math. Helv. 63 (1994), 575-611. | Zbl 0832.16008
[005] [6] W. Crawley-Boevey, On tame algebras and bocses, Proc. London Math. Soc. 56 (1988), 451-483. | Zbl 0661.16026
[006] [7] E D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer, 1995. | Zbl 0819.13001
[007] [8] A. Grothendieck et J. A. Dieudonné, Éléments de géométrie algébrique IV, Inst. Hautes Études Sci. Publ. Math. 32 (1967). | Zbl 0203.23301
[008] [9] R. Hartshorn, Algebraic Geometry, Springer, 1977.
[009] [10] W. Hesselink, Singularities in the nilpotent scheme of a classical group, Trans. Amer. Math. Soc. 222 (1976), 1-32. | Zbl 0332.14017
[010] [11] K J. T. Knight, On epimorphisms of non-commutative rings, Proc. Cambridge Philos. Soc. 68 (1970), 589-600. | Zbl 0216.33302
[011] [12] H. Kraft and C. Procesi, Minimal singularities in , Invent. Math. 62 (1981), 503-515. | Zbl 0478.14040
[012] [13] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.
[013] [14] L. Silver, Noncommutative localizations and applications, J. Algebra 7 (1967), 44-76. | Zbl 0173.03305
[014] [15] P. Slodowy, Simple Singularities and Simple Algebraic Groups, Lecture Notes in Math. 815, Springer, 1980. | Zbl 0441.14002