ON THE GEOMETRY OF BIHYPERELLIPTIC CURVES

Title & Authors
ON THE GEOMETRY OF BIHYPERELLIPTIC CURVES
Ballico, Edoardo; Casnati, Gianfranco; Fontanari, Claudio;

Abstract
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 $\small{g{\geq}4{\gamma}+2{\geq}10}$.
Keywords
curves;moduli;cover;unirationality;
Language
English
Cited by
References
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

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

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

6.
M. Cornalba, On the locus of curves with automorphisms, Ann. Mat. Pura Appl. (4) 149 (1987), 135-151

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

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

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