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A proof of Noether’s formula for the arithmetic genus of an algebraic surface. (English) Zbl 0399.14004

MSC:
14C40 Riemann-Roch theorems
14J99 Surfaces and higher-dimensional varieties
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References:
[1] T. Bonnesen : Sur les séries linéaires triplement infinies de courbes algébriques sur une surface algébrique , Bull. Acad. Royale des Sciences et des Lettres de Danemark, 4 (1906) 281-293. · JFM 38.0647.02
[2] A. Cayley : Memoir on the theory of reciprocal surfaces , Phil. Trans. Royal Soc. of London, 159 (1869) 201-229, Papers 6, 329-358. · JFM 02.0556.04
[3] A. Cayley : On the rational transformation between two spaces , Proc. London Math. Soc., 3 (1870) 127-180, Papers 7, 189-240. · JFM 03.0430.01
[4] A. Cayley : On the deficiency of certain surfaces , Math. Ann., 3 (1871) 526-529, Papers 8, 394-397. · JFM 03.0373.01
[5] M.A. Clebsch : Sur les surfaces algébriques , C.R. Acad. Sci. Paris, 67 (1868) 1238-1239. · JFM 01.0234.02
[6] G. Kempf and D. Laksov : The determinantal formula of Schubert calculus , Acta Math., 132 (1974) 153-162. · Zbl 0295.14023
[7] S. Kleiman : The enumerative theory of singularities, Real and complex singularities , Oslo 1976, Sijthoff & Noordhoff International Publishers. · Zbl 0385.14018
[8] M. Noether : Sulle curve multiple di superficie algebriche , Ann. d. Mat., 5 (1871-1873) 163-177. · JFM 04.0423.02
[9] M. Noether : Zur Theorie des eindeutigen Entsprechens algebraischer Gebilde , Math. Ann., 2 (1870) 293-316; 8 (1875) 495-533. · JFM 02.0619.01
[10] J. Roberts : Generic projections of algebraic varieties , Amer. J. Math., 93 (1971) 191-214. · Zbl 0212.53801
[11] J. Roberts : The variation of singular cycles in an algebraic family of morphisms , Trans. AMS, 168 (1972) 153-164. · Zbl 0241.14005
[12] C. Segre : ” Intorno ad un carattere delle superficie et delle varietà superiori algebriche , Atti. Acc. Torino, 31 (1896) 341-357. · JFM 27.0454.01
[13] O. Zariski : Algebraic surfaces . Springer, Berlin etc. (1971). · Zbl 0219.14020
[14] H.G. Zeuthen : Études géometriques de quelques-unes des propriétés de deux surfaces dont les points se correspondent un à un , Math. Ann. 4 (1871) 21-49. · JFM 04.0424.02
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