DOI QR코드

DOI QR Code

TETRAGONAL MODULAR CURVES X1(M, N)

  • Jeon, Dae-Yeol (DEPARTMENT OF MATHEMATICS EDUCATION KONGJU NATIONAL UNIVERSITY)
  • 발행 : 2008.07.31

초록

In this work, we determine all the modular curves $X_1$(M, N) which are tetragonal.

키워드

참고문헌

  1. D. Abramovich, A linear lower bound on the gonality of modular curves, Int. Math. Res. Not. 1996 (1996), no. 20, 1005-1011 https://doi.org/10.1155/S1073792896000621
  2. M. H. Baker, E. Gonzalez-Jimenez, J. Gonzalez, and B. Poonen, Finiteness results for modular curves of genus at least 2, Amer. J. Math. 127 (2005), no. 6, 1325-1387 https://doi.org/10.1353/ajm.2005.0037
  3. M. Coppens and G. Martens, Secant spaces and Clifford's theorem, Compositio Math. 78 (1991), 193-212
  4. M. Green, Koszul cohomology and the geometry of projective varieties I, J. Differ. Geom. 19 (1984), 125-171 https://doi.org/10.4310/jdg/1214438426
  5. M. Green and R. Lazarsfeld, Some results on the syzygies of finite sets and algebraic curves, Compositio Math. 67 (1988), 301-314
  6. Y. Hasegawa and M. Shimura, Trigonal modular curves, Acta Arith. 88 (1999), 129-140 https://doi.org/10.4064/aa-88-2-129-140
  7. N. Ishii and F. Momose, Hyperelliptic modular curves, Tsukuba J. Math. 15 (1991), 413-423 https://doi.org/10.21099/tkbjm/1496161667
  8. D. Jeon and C. H. Kim, On the arithmetic of certain modular curves, Acta Arith. 130 (2007), no. 2, 181-193 https://doi.org/10.4064/aa130-2-7
  9. D. Jeon, C. H. Kim, and E. Park, On the torsion of elliptic curves over quartic number fields, J. London Math. Soc. (2) 74 (2006), no. 1, 1-12 https://doi.org/10.1112/S0024610706022940
  10. William A. Stein, http://modular.fas.harvard.edu.