Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

On the existence of plane curves with prescribed singularities


Author: Gerald B. Huff
Journal: Bull. Amer. Math. Soc. 57 (1951), 411-419
MathSciNet review: 0044147
Full-text PDF

References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. Arthur B. Coble, Algebraic geometry and theta functions, Revised printing. American Mathematical Society Colloquium Publication, vol. X, American Mathematical Society, Providence, R.I., 1961. MR 0123958
  • 2. A. B. Coble, Cremona transformations..., Bull. Amer. Math. Soc. vol. 28 (1922) p. 335.
  • 3. A. B. Coble, Cremona's diophantine equations, Amer. J. Math. vol. 56 (1934) p. 487.
  • 4. J. L. Coolidge, Algebraic plane curves, Oxford, 1931, p. 487.
  • 5. L. Cremona, Sulle transformazioni geometriche delle figure piane, Giornale di Matematiche vol. 1 (1863) p. 306.
  • 6. P. Du Val, On the Kantor group of a set of points in the plane, Proc. London Math. Soc. (2) vol. 42 (1936) pp. 18-51.
  • 7. G. B. Huff, A note on Cremona transformations, Proc. Nat. Acad. Sci. U.S.A. vol. 20 (1934) p. 429.
  • 8. G. B. Huff, Inequalities connecting solutions of Cremona’s equations, Bull. Amer. Math. Soc. 52 (1946), 287–291. MR 0015859, 10.1090/S0002-9904-1946-08559-6
  • 9. G. B. Huff, An arithmetic characterization of proper characteristics of linear systems, Amer. J. Math. 68 (1946), 681–688. MR 0018880
  • 10. Gerald B. Huff, Cremona’s equations and the properness inequalities, Duke Math. J. 17 (1950), 385–389. MR 0041472
  • 11. Gerald B. Huff, The completion of a theorem of Kantor, Bull. Amer. Math. Soc. 50 (1944), 692–696. MR 0012818, 10.1090/S0002-9904-1944-08208-6
  • 12. E. de Jonquieres, Solution d'une question d'analyse indéterminée, C. R. Acad. Sci. Paris vol. 101 (1885) p. 857.
  • 13. S. Kantor, Premier fondements pour une théorie des transformations univoques..., Naples, 1891, p. 297.
  • 14. I. Larice, Due nuove soluzioni generali... delle equazioni di condizione della trasformazioni Cremoniani, Periodico di Matematica per l'Insegnamento Secondario (3) vol. 6, p. 234.
  • 15. Solomon Lefschetz, On the existence of loci with given singularities, Trans. Amer. Math. Soc. 14 (1913), no. 1, 23–41. MR 1500934, 10.1090/S0002-9947-1913-1500934-0
  • 16. M. Noether, Ueber Flächen, welche Schaaren rationaler Kurven besitzen, Math. Ann. vol. 3 (1871) p. 166.
  • 17. F. P. Ruffini, Risoluzione di 2 equazione... di trasformazione Cremoniana, Memorie della R. Accademia delle scienze dell'Istituto di Bologna vol. 8 (1877) p. 483.
  • 18. G. Salmon and O. W. Fiedler, Analytische Geometrie der höheren ebenen Kurven, Leipzig, 1882, p. 83.
  • 19. Mildred E. Taylor, A Determination of the Types of Planar Cremona Transformations with not More than 9 𝐹-Points, Amer. J. Math. 54 (1932), no. 1, 123–128. MR 1506879, 10.2307/2371083
  • 20. G. Veronese, ...das Princip des Projicirens und Schneidens..., Math. Ann. vol. 19 (1882) p. 211.
  • 21. Oscar Zariski, On the irregularity of cyclic multiple planes, Ann. of Math. (2) 32 (1931), no. 3, 485–511. MR 1503012, 10.2307/1968247
  • 22. Oscar Zariski, Algebraic surfaces, Classics in Mathematics, Springer-Verlag, Berlin, 1995. With appendices by S. S. Abhyankar, J. Lipman and D. Mumford; Preface to the appendices by Mumford; Reprint of the second (1971) edition. MR 1336146


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1951-09542-7