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References
M. F. Atiyah, “Vector bundles over an elliptic curve,” Proc. London Math. Soc., vol. 7, pp. 414–452, 1957.
M. Auslander and I. Reiten, “Representation theory of Artin algebras III,” Comm. Algebra, vol. 3, pp. 239–294, 1975.
M. Auslander, “Functors and morphisms determined by objects and applications of morphisms determined by modules,” Proc. conf. representation theory, Philadelphia 1976, pp. 1–244, Marcel Dekker, New York, 1978.
M. Auslander, “Rational singularities and almost split sequences,” Trans. Amer. Math. Soc., vol. 293, pp. 511–532, 1986.
A. A. Beilinson, “Coherent sheaves on P n and problems of linear algebra,” Funct. Anal. Appl., vol. 12, pp. 214–216, 1979.
M. Beltrametti and L. Robbiano, Introduction to the theory of weighted projective spaces, Preprint MPI Bonn, 1985.
K. Bongartz, “Tilted algebras,” Representations of algebras, pp. 26–38, Springer-Verlag, Berlin-Heidelberg-New York, 1981. Lecture Notes in Mathematics 903.
C. Delorme, “Espaces projectifs anisotropes,” Bull. Soc. Math. France, vol. 103, pp. 203–223, 1975.
V. Dlab and C. M. Ringel, “Indecomposable representations of graphs and algebras,” Mem. Amer. Math. Soc., vol. 173, 1976.
I. Dolgachev, “Weighted projective varieties,” Group actions and vector fields, pp. 34–71, Springer-Verlag, Berlin-Heidelberg-New York, 1982. Lecture Notes in Mathematics 956.
P. Donovan and M. R. Freislich, The representation theory of finite graphs and associative algebras, Ottawa, 1973. Carleton Lecture Notes 5.
P. Gabriel, “Des catégories abéliennes.,” Bull. Soc. math. France, vol. 90, pp. 323–448, 1967.
P. Gabriel, “Indecomposable representations II,” Symposia Math. Ist. Naz. Alta Mat., vol. 11, pp. 81–107, 1973.
P. Gabriel, “Auslander-Reiten sequences and representation-finite algebras,” Proceedings Ottawa 1979, pp. 1–71, Springer-Verlag, Berlin-Heidelberg-New York, 1980.
R. Godement, Théorie des faisceaux, Hermann, Paris, 1973.
A. Grothendieck, “Sur la classification des fibrés holomorphes sur la surface de Riemann,” Amer. J. Math., vol. 79, pp. 121–138, 1957.
A. Grothendieck, Eléments de géométrie algébrique II, Publications Mathématiques 8, Institut des Hautes Etudes Scientifiques, Paris, 1961.
A. Grothendieck, Eléments de géométrie algébrique III, Publications Mathématiques 11, Institut des Hautes Etudes Scientifiques, Paris, 1961.
D. Happel, U. Preiser, and C. M. Ringel, “Binary polyhedral groups and Euclidean diagrams,” Manuscripta math., vol. 31, pp. 317–329, 1980.
D. Happel and C. M. Ringel, “Tilted Algebras,” Trans. Amer. Math. Soc., vol. 274, pp. 399–443, 1982.
D. Happel, “Triangulated categories in representation theory of finite dimensional algebras,” Comm. Math. Helv., 1986. To appear.
D. Happel and C. M. Ringel, “The derived category of a tubular algebra,” Representation theory I, Finite dimensional algebras, pp. 156–180, Springer-Verlag, Berlin-Heidelberg-New York, 1986. Lecture Notes in Mathematics 1177.
R. Hartshorne, Residues and duality, Lecture Notes in Mathematics 20, Springer-Verlag, Berlin-Heidelberg-New York, 1966.
R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
F. Klein, Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, Teubner, Leipzig, 1884.
H. Lenzing, “Curve singularities arising from the representation theory of tame hereditary Artin algebras,” Representation theory I. Finite dimensional Algebras, pp. 199–231, Springer-Verlag, Berlin-Heidelberg-New York, 1986. Lecture Notes in Mathematics 1177.
S. Mori, “Graded factorial domains,” Japan. J. Math., vol. 3, pp. 223–238, 1977.
L. A. Nazarova, “Representations of quivers of infinite type,” Izv. Akad. Nauk SSR, Ser. Math., vol. 37, pp. 752–791, 1973.
T. Oda, “Vector bundles on an elliptic curve,” Nagoya Math. J., vol. 43, pp. 41–72, 1971.
C. M. Ringel, Tame algebras and integral quadratic forms, Springer, Berlin-Heidelberg-New York, 1984. Lecture Notes in Mathematics 1099.
J.-P. Serre, “Faisceaux algébriques cohérents,” Annals of Math., vol. 61, pp. 197–278, 1955.
C. S. Seshadri, “Fibrés vectoriels sur les courbes algébriques,” Astérisque, vol. 96, pp. 1–209, 1982.
P. Slodowy, “Platonic solids, Kleinian singularities and Lie groups,” Algebraic Geometry, pp. 102–138, Springer-Verlag, Heidelberg-New York, 1983. Lecture Notes in Mathematics 1008.
J. L. Verdier, “Catégories dérivés, etat 0,” Séminaire géométrie algébrique, 4 1/2, pp. 262–311, Springer-Verlag, Berlin-Heidelberg-New York, 1977. Lecture Notes in Mathematics 569.
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Geigle, W., Lenzing, H. (1987). A class of weighted projective curves arising in representation theory of finite dimensional algebras. In: Greuel, GM., Trautmann, G. (eds) Singularities, Representation of Algebras, and Vector Bundles. Lecture Notes in Mathematics, vol 1273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078849
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DOI: https://doi.org/10.1007/BFb0078849
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