A proof of Noether's formula for the arithmetic genus of an algebraic surface

Ragni Piene

Compositio Mathematica (1979)

  • Volume: 38, Issue: 1, page 113-119
  • ISSN: 0010-437X

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Piene, Ragni. "A proof of Noether's formula for the arithmetic genus of an algebraic surface." Compositio Mathematica 38.1 (1979): 113-119. <http://eudml.org/doc/89389>.

@article{Piene1979,
author = {Piene, Ragni},
journal = {Compositio Mathematica},
keywords = {Arithmetic Genus; Smooth Proper Surface; Hirzebruch's Riemann-Roch Theorem},
language = {eng},
number = {1},
pages = {113-119},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {A proof of Noether's formula for the arithmetic genus of an algebraic surface},
url = {http://eudml.org/doc/89389},
volume = {38},
year = {1979},
}

TY - JOUR
AU - Piene, Ragni
TI - A proof of Noether's formula for the arithmetic genus of an algebraic surface
JO - Compositio Mathematica
PY - 1979
PB - Sijthoff et Noordhoff International Publishers
VL - 38
IS - 1
SP - 113
EP - 119
LA - eng
KW - Arithmetic Genus; Smooth Proper Surface; Hirzebruch's Riemann-Roch Theorem
UR - http://eudml.org/doc/89389
ER -

References

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  1. [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. Zbl38.0647.02JFM38.0647.02
  2. [2] A. Cayley: Memoir on the theory of reciprocal surfaces, Phil. Trans. Royal Soc. of London, 159 (1869) 201-229, Papers 6, 329-358. JFM02.0556.04
  3. [3] A. Cayley: On the rational transformation between two spaces, Proc. London Math. Soc., 3 (1870) 127-180, Papers 7, 189-240. JFM03.0430.01
  4. [4] A. Cayley: On the deficiency of certain surfaces, Math. Ann., 3 (1871) 526-529, Papers 8, 394-397. Zbl03.0373.01MR1509720JFM03.0373.01
  5. [5] M.A. Clebsch: Sur les surfaces algébriques, C.R. Acad. Sci. Paris, 67 (1868) 1238-1239. Zbl01.0234.02JFM01.0234.02
  6. [6] G. Kempf and D. Laksov: The determinantal formula of Schubert calculus, Acta Math., 132 (1974) 153-162. Zbl0295.14023MR338006
  7. [7] S. Kleiman: The enumerative theory of singularities, Real and complex singularities, Oslo1976, Sijthoff & Noordhoff International Publishers. Zbl0385.14018MR568897
  8. [8] M. Noether: Sulle curve multiple di superficie algebriche, Ann. d. Mat., 5 (1871-1873) 163-177. JFM04.0423.02
  9. [9] M. Noether: Zur Theorie des eindeutigen Entsprechens algebraischer Gebilde, Math. Ann., 2 (1870) 293-316; 8 (1875) 495-533. MR1509663JFM02.0619.01
  10. [10] J. Roberts: Generic projections of algebraic varieties, Amer. J. Math., 93 (1971) 191-214. Zbl0212.53801MR277530
  11. [11] J. Roberts: The variation of singular cycles in an algebraic family of morphisms, Trans. AMS, 168 (1972) 153-164. Zbl0241.14005MR306199
  12. [12] C. Segre: "Intorno ad un carattere delle superficie et delle varietà superiori algebriche, Atti. Acc. Torino, 31 (1896) 341-357. Zbl27.0454.01JFM27.0454.01
  13. [13] O. Zariski: Algebraic surfaces. Springer, Berlin etc. (1971). Zbl0219.14020MR469915
  14. [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. Zbl04.0424.02MR1509729JFM04.0424.02

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