Geometric structures on toroidal maps and elliptic curves

David Singerman; Robert I. Syddall

Mathematica Slovaca (2000)

  • Volume: 50, Issue: 5, page 495-512
  • ISSN: 0139-9918

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Singerman, David, and Syddall, Robert I.. "Geometric structures on toroidal maps and elliptic curves." Mathematica Slovaca 50.5 (2000): 495-512. <http://eudml.org/doc/34523>.

@article{Singerman2000,
author = {Singerman, David, Syddall, Robert I.},
journal = {Mathematica Slovaca},
keywords = {graph embedding; toroidal map; elliptic curve; Riemann surface},
language = {eng},
number = {5},
pages = {495-512},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Geometric structures on toroidal maps and elliptic curves},
url = {http://eudml.org/doc/34523},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Singerman, David
AU - Syddall, Robert I.
TI - Geometric structures on toroidal maps and elliptic curves
JO - Mathematica Slovaca
PY - 2000
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 50
IS - 5
SP - 495
EP - 512
LA - eng
KW - graph embedding; toroidal map; elliptic curve; Riemann surface
UR - http://eudml.org/doc/34523
ER -

References

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  1. BELYI G. V., On Galois extensions of a maximal cyclotomic field, Izv. Akad. Nauk SSSR 43 (1979), 269-276 (Russian) [English translation: Math. USSR-Izv. 14 (1980), 247-256]. (1979) Zbl0409.12012MR0534593
  2. BEAZLEYCOHEN P.-ITZYKSON C.-WOLFART J., Fuchsian triangle groups and Grothendieck Dessins. Variations on a theme of Belyi, Comm. Math. Phys. 163 (1994), 605-627. (1994) MR1284798
  3. COXETER H. S. M.-MOSER W. O. J., Generators and Relations for Discrete Groups, Springer-Verlag, Berlin, 1965. (1965) Zbl0133.28002MR0174618
  4. GRIFFITHS P. A., Introduction to Algebraic Curves, (2nd ed.). Transl. Math. Monographs 76, Amer. Math. Soc, Providence, RI, 1996 (Transl. from the Chinese by Kuniko Weltin). (1996) Zbl0873.14030MR1013999
  5. GROTHENDIECK A., Esquisse ďun programme, In: Geometric Galois Actions 1 (L. Schneps, P. Lochak, eds.), London Math. Soc. Lecture Note Ser. 242, Cambridge University Press, Cambridge, 1997. (1997) MR1483106
  6. JONES G. A.-SINGERMAN D., Theory of maps on orientable surfaces, Proc. London Math. Soc. (3) 37 (1978), 273-307. (1978) Zbl0391.05024MR0505721
  7. JONES G. A.-SINGERMAN D., Complex Functions, an Algebraic and Geometric Viewpoint, Cambridge University Press, Cambridge, 1987. (1987) Zbl0608.30001MR0890746
  8. JONES G. A.-SINGERMAN D., Belyi functions, hypermaps and Galois groups, Bull. London Math. Soc. 28 (1996), 561-590. (1996) Zbl0853.14017MR1405488
  9. KNAPP A. W., Elliptic curves, In: Math. Notes 40, Princeton Univ.Press, Princeton, NJ, 1992. (1992) Zbl0804.14013MR1193029
  10. MAGNUS W., Noneuclidean Tesselations and Their Groups, Academic Press, New York, 1974. (1974) Zbl0293.50002MR0352287
  11. SINGERMAN D.-SYDDALL R. I., Belyi uniformization of elliptic curves, Bull. London Math. Soc. 29 (1997), 443-451. (1997) Zbl0868.14019MR1446563
  12. STARK H. M., A complete determination of the complex quadratic fields of class number one, Michigan Math. J. 14 (1967), 1-27. (1967) Zbl0148.27802MR0222050
  13. SYDDALL R. I., Uniform maps on the torus, European J. Combin. (To appear). 
  14. WOLFART J., The obvious' part of Belyi's Theorem and Riemann surfaces with many automorphisms, In: Geometric Galois Actions 1 (L. Schneps, P. Lochak, eds.), London Math. Soc. Lecture Note Ser. 242, Cambridge University Press, Cambridge, 1997. (1997) Zbl0915.14021MR1483112

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