Geometry of regular modules over canonical algebras
HTML articles powered by AMS MathViewer
- by Grzegorz Bobiński PDF
- Trans. Amer. Math. Soc. 360 (2008), 717-742 Request permission
Abstract:
We classify canonical algebras such that for every dimension vector of a regular module the corresponding module variety is normal (respectively, a complete intersection). We also prove that for the dimension vectors of regular modules normality is equivalent to irreducibility.References
- M. Barot and Jan Schröer, Module varieties over canonical algebras, J. Algebra 246 (2001), no. 1, 175–192. MR 1872616, DOI 10.1006/jabr.2001.8933
- Grzegorz Bobiński and Andrzej Skowroński, Geometry of modules over tame quasi-tilted algebras, Colloq. Math. 79 (1999), no. 1, 85–118. MR 1671811, DOI 10.4064/cm-79-1-85-118
- Grzegorz Bobiński and Andrzej Skowroński, Geometry of periodic modules over tame concealed and tubular algebras, Algebr. Represent. Theory 5 (2002), no. 2, 187–200. MR 1909550, DOI 10.1023/A:1015606729502
- Klaus Bongartz, Algebras and quadratic forms, J. London Math. Soc. (2) 28 (1983), no. 3, 461–469. MR 724715, DOI 10.1112/jlms/s2-28.3.461
- Klaus Bongartz, Minimal singularities for representations of Dynkin quivers, Comment. Math. Helv. 69 (1994), no. 4, 575–611. MR 1303228, DOI 10.1007/BF02564505
- Klaus Bongartz, On degenerations and extensions of finite-dimensional modules, Adv. Math. 121 (1996), no. 2, 245–287. MR 1402728, DOI 10.1006/aima.1996.0053
- Klaus Bongartz, Some geometric aspects of representation theory, Algebras and modules, I (Trondheim, 1996) CMS Conf. Proc., vol. 23, Amer. Math. Soc., Providence, RI, 1998, pp. 1–27. MR 1648601
- William Crawley-Boevey and Jan Schröer, Irreducible components of varieties of modules, J. Reine Angew. Math. 553 (2002), 201–220. MR 1944812, DOI 10.1515/crll.2002.100
- Mátyás Domokos and Helmut Lenzing, Invariant theory of canonical algebras, J. Algebra 228 (2000), no. 2, 738–762. MR 1764590, DOI 10.1006/jabr.2000.8298
- M. Domokos and H. Lenzing, Moduli spaces for representations of concealed-canonical algebras, J. Algebra 251 (2002), no. 1, 371–394. MR 1900290, DOI 10.1006/jabr.2001.9117
- Werner Geigle and Helmut Lenzing, A class of weighted projective curves arising in representation theory of finite-dimensional algebras, Singularities, representation of algebras, and vector bundles (Lambrecht, 1985) Lecture Notes in Math., vol. 1273, Springer, Berlin, 1987, pp. 265–297. MR 915180, DOI 10.1007/BFb0078849
- Christof Geiß, Geometric methods in representation theory of finite-dimensional algebras, Representation Theory of Algebras and Related Topics (Mexico City, 1994), 1996, pp. 53–63.
- Dieter Happel, A characterization of hereditary categories with tilting object, Invent. Math. 144 (2001), no. 2, 381–398. MR 1827736, DOI 10.1007/s002220100135
- Dieter Happel, Idun Reiten, and Sverre O. Smalø, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 120 (1996), no. 575, viii+ 88. MR 1327209, DOI 10.1090/memo/0575
- Hanspeter Kraft, Geometrische Methoden in der Invariantentheorie, Aspects of Mathematics, D1, Friedr. Vieweg & Sohn, Braunschweig, 1984 (German). MR 768181, DOI 10.1007/978-3-322-83813-1
- Hanspeter Kraft, Geometric methods in representation theory, Representations of algebras (Puebla, 1980) Lecture Notes in Math., vol. 944, Springer, Berlin-New York, 1982, pp. 180–258. MR 672117
- Helmut Lenzing and José Antonio de la Peña, Concealed-canonical algebras and separating tubular families, Proc. London Math. Soc. (3) 78 (1999), no. 3, 513–540. MR 1674837, DOI 10.1112/S0024611599001872
- Markus Reineke, The monoid of families of quiver representations, Proc. London Math. Soc. (3) 84 (2002), no. 3, 663–685. MR 1888427, DOI 10.1112/S0024611502013497
- Claus Michael Ringel, The rational invariants of the tame quivers, Invent. Math. 58 (1980), no. 3, 217–239. MR 571574, DOI 10.1007/BF01390253
- Claus Michael Ringel, Tame algebras and integral quadratic forms, Lecture Notes in Mathematics, vol. 1099, Springer-Verlag, Berlin, 1984. MR 774589, DOI 10.1007/BFb0072870
- Andrzej Skowroński, On omnipresent tubular families of modules, Representation theory of algebras (Cocoyoc, 1994) CMS Conf. Proc., vol. 18, Amer. Math. Soc., Providence, RI, 1996, pp. 641–657. MR 1388078
- Andrzej Skowroński and Jerzy Weyman, Semi-invariants of canonical algebras, Manuscripta Math. 100 (1999), no. 3, 391–403. MR 1726226, DOI 10.1007/s002290050208
- Detlef Voigt, Induzierte Darstellungen in der Theorie der endlichen, algebraischen Gruppen, Lecture Notes in Mathematics, Vol. 592, Springer-Verlag, Berlin-New York, 1977 (German). Mit einer englischen Einführung. MR 0486168, DOI 10.1007/BFb0086128
Additional Information
- Grzegorz Bobiński
- Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland
- ORCID: 0000-0002-1770-2290
- Email: gregbob@mat.uni.torun.pl
- Received by editor(s): May 16, 2005
- Received by editor(s) in revised form: October 4, 2005
- Published electronically: August 30, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 717-742
- MSC (2000): Primary 16G20; Secondary 14L30
- DOI: https://doi.org/10.1090/S0002-9947-07-04174-8
- MathSciNet review: 2346469
Dedicated: Dedicated to the memory of Professor Stanisław Balcerzyk