On the existence of plane curves with prescribed singularities
Author:
Gerald B. Huff
Journal:
Bull. Amer. Math. Soc. 57 (1951), 411-419
DOI:
https://doi.org/10.1090/S0002-9904-1951-09542-7
MathSciNet review:
0044147
Full-text PDF Free Access
References | Additional Information
- Arthur B. Coble, Algebraic geometry and theta functions, American Mathematical Society Colloquium Publications, Vol. X, American Mathematical Society, Providence, R.I., 1961. Revised printing. 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.
- G. B. Huff, Inequalities connecting solutions of Cremona’s equations, Bull. Amer. Math. Soc. 52 (1946), 287–291. MR 15859, DOI https://doi.org/10.1090/S0002-9904-1946-08559-6
- G. B. Huff, An arithmetic characterization of proper characteristics of linear systems, Amer. J. Math. 68 (1946), 681–688. MR 18880, DOI https://doi.org/10.2307/2371792
- Gerald B. Huff, Cremona’s equations and the properness inequalities, Duke Math. J. 17 (1950), 385–389. MR 41472
- Gerald B. Huff, The completion of a theorem of Kantor, Bull. Amer. Math. Soc. 50 (1944), 692–696. MR 12818, DOI https://doi.org/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.
- Solomon Lefschetz, On the existence of loci with given singularities, Trans. Amer. Math. Soc. 14 (1913), no. 1, 23–41. MR 1500934, DOI https://doi.org/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.
- 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, DOI https://doi.org/10.2307/2371083 20. G. Veronese, ...das Princip des Projicirens und Schneidens..., Math. Ann. vol. 19 (1882) p. 211.
- Oscar Zariski, On the irregularity of cyclic multiple planes, Ann. of Math. (2) 32 (1931), no. 3, 485–511. MR 1503012, DOI https://doi.org/10.2307/1968247
- 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
