대한수학회지 (Journal of the Korean Mathematical Society)

  • 제44권6호
  • /
  • Pages.1339-1350
  • /
  • 2007
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON THE GEOMETRY OF BIHYPERELLIPTIC CURVES

  • 발행 : 2007.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Here we consider bihyperelliptic curves, i.e., double covers of hyperelliptic curves. By applying the theory of quadruple covers, among other things we prove that the bihyperelliptic locus in the moduli space of smooth curves is irreducible and unirational $g{\geq}4{\gamma}+2{\geq}10$.

키워드

참고문헌

  1. R. Accola, Topics in the theory of Riemann surfaces, Lecture Notes in Mathematics, 1595. Springer-Verlag, Berlin, 1994
  2. G. Casnati, Covers of algebraic varieties. III. The discriminant of a cover of degree 4 and the trigonal construction, Trans. Amer. Math. Soc. 350 (1998), no. 4, 1359-1378 https://doi.org/10.1090/S0002-9947-98-02136-9
  3. G. Casnati and A. Del Centina, A characterization of bielliptic curves and applications to their moduli spaces, Ann. Mat. Pura Appl. (4) 181 (2002), no. 2, 213-221 https://doi.org/10.1007/s102310100036
  4. G. Casnati and T. Ekedahl, Covers of algebraic varieties. I. A general structure theorem, covers of degree 3 4 and Enriques surfaces, J. Algebraic Geom. 5 (1996), no. 3, 439-460
  5. G. Chaves, Revetements ramifies de la droite projective complexe, Math. Z. 226 (1997), no. 1, 67-84 https://doi.org/10.1007/PL00004334
  6. M. Cornalba, On the locus of curves with automorphisms, Ann. Mat. Pura Appl. (4) 149 (1987), 135-151 https://doi.org/10.1007/BF01773930
  7. M. Cornalba and L. Stoppino, A sharp bound for the slope of double cover fibrations, Preprint arXiv:math.AG/0510144
  8. A. Del Centina and A. Gimigliano, Scrollar invariants and resolutions of certain d-gonal curves, Ann. Univ. Ferrara Sez. VII (N.S.) 39 (1993), 187-201 (1995)
  9. A. Del Centina and A. Gimigliano, Corrigenda to: 'Scrollar invariants and resolutions of certain d-gonal curves' [Ann. Univ. Ferrara Sez. VII (N.S.) 39 (1993), 187{201 (1995)], Ann. Univ. Ferrara Sez. VII (N.S.) 41 (1995), 147 (1997)
  10. R. Donagi, The fibers of the Prym map, Contemp. Math. 136 (1992), 55-125 https://doi.org/10.1090/conm/136/1188194
  11. D. Glass and R. Pries, On the moduli space of Klein four covers of the projective line, Computational aspects of algebraic curves, 58-70, Lecture Notes Ser. Comput., 13, World Sci. Publ., Hackensack, NJ, 2005
  12. R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52. Springer- Verlag, New York-Heidelberg, 1977
  13. R. Lazarsfeld, A Barth-type theorem for branched coverings of projective space, Math. Ann. 249 (1980), no. 2, 153-162 https://doi.org/10.1007/BF01351412
  14. V. L. Popov and E. B. Vinberg, Invariant theory, Algebraic Geometry IV, edited by A.N. Parshin and I. R. Shafarevich, Encyclopedia of Mathematical Sciences, 55, 1991