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Schottky's form and the hyperelliptic locus


Author: Cris Poor
Journal: Proc. Amer. Math. Soc. 124 (1996), 1987-1991
MSC (1991): Primary 11F46; Secondary 14K25, 11E45
DOI: https://doi.org/10.1090/S0002-9939-96-03312-6
MathSciNet review: 1327038
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Abstract: We show that Schottky's modular form, $J_{g}$, has in every genus an irreducible divisor which contains the hyperelliptic locus. We also improve a corollary of Igusa concerning Siegel modular forms that must necessarily vanish on the hyperelliptic locus.


References [Enhancements On Off] (What's this?)

  • 1. J. H. Conway, and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Grund. der math. Wiss. 290, Springer--Verlag, New York, 1993. MR 93h:11069
  • 2. E. Freitag, Die Irreduzibilität der Schottkyrelation (Bemerkung zu einen Satz von J. Igusa), Arch. Math. 40 (1983), 255-259. MR 84m:14034
  • 3. J. I. Igusa, Modular forms and projective invariants, Amer. J. Math. 89 (1967), 817-855. MR 37:5217
  • 4. J. I. Igusa, On the irreducibility of Schottky's divisor, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), 531--545. MR 83f:14023
  • 5. J. I. Igusa, Schottky's invariant and quadratic forms, Christoffel Symposium, Birkhäuser Verlag, 1981, pp. 352--362. MR 83m:10031
  • 6. J. I. Igusa, Theta Functions, Grundlehren der math. Wiss., Springer Verlag 194, 1972. MR 48:3972
  • 7. S. Tsuyumine, On Siegel modular forms of degree three, Amer. J. Math. 108 (1986), 755-862, 1001-1003. MR 88a:11047a,b
  • 8. E. Witt, Eine Identität zwischen Modulformen zweiten Grades, Abhandlungen aus dem Math. Sem. Hansischen Universität 14 (1941), 323-337. MR 3:163d

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Additional Information

Cris Poor
Affiliation: Department of Mathematics, Fordham University, Bronx, New York 10458
Email: poor@murray.fordham.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03312-6
Keywords: Analytic class invariant, theta series, hyperelliptic
Received by editor(s): October 24, 1994
Received by editor(s) in revised form: January 30, 1995
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society

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