The universal periods of curves and the Schottky problem

Takashi Ichikawa

Compositio Mathematica (1993)

  • Volume: 85, Issue: 1, page 1-8
  • ISSN: 0010-437X

How to cite


Ichikawa, Takashi. "The universal periods of curves and the Schottky problem." Compositio Mathematica 85.1 (1993): 1-8. <>.

author = {Ichikawa, Takashi},
journal = {Compositio Mathematica},
keywords = {Schottky problem; Siegel modular forms; Jacobian locus; periods of algebraic curves},
language = {eng},
number = {1},
pages = {1-8},
publisher = {Kluwer Academic Publishers},
title = {The universal periods of curves and the Schottky problem},
url = {},
volume = {85},
year = {1993},

AU - Ichikawa, Takashi
TI - The universal periods of curves and the Schottky problem
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 85
IS - 1
SP - 1
EP - 8
LA - eng
KW - Schottky problem; Siegel modular forms; Jacobian locus; periods of algebraic curves
UR -
ER -


  1. [1] P. Deligne and D. Mumford: The irreducibility of the space of curves of given genus, Publ. Math. IHES.36 (1969), 75-109. Zbl0181.48803MR262240
  2. [2] G. Faltings: Arithmetische Kompaktifizierung des Modulraums der abelschen Varietäten, Proc. Arbeitstagung Bonn 1984, Lecture Notes in Math. 1111 (1985), 321-383, Springer-Verlag. Zbl0597.14036MR797429
  3. [3] J.D. Fay: Theta functions on Riemann surfaces, Lecture Notes in Math.352 (1973), Springer-Verlag. Zbl0281.30013MR335789
  4. [4] L. Gerritzen: Zur analytischen Beschreibung des Raumes der Schottky-Mumford-Kurven, Math. Ann.255 (1981), 259-271. Zbl0442.14007MR614401
  5. [5] Y. Ihara: On discrete subgroups of the 2 x 2 projective linear group over p-adic fields, J. Math. Soc. Japan18 (1966), 219-235. Zbl0158.27702MR223463
  6. [6] P. Koebe: Über die Uniformisierung der algebraischen Kurven IV, Math. Ann.75 (1914), 42-129. Zbl45.0669.01MR1511787JFM45.0669.01
  7. [7] Yu. I. Manin and V. Drinfeld: Periods of p-adic Schottky groups, J. Reine Angew. Math.262/263 (1972), 239-247. Zbl0275.14017MR396582
  8. [8] D. Mumford: An analytic construction of degenerating curves over complete local fields, Comp. Math.24 (1972), 129-174. Zbl0228.14011MR352105
  9. [9] D. Mumford: Tata lectures on theta II, Progress in Math.43 (1984), Birkhäuser. Zbl0549.14014MR742776
  10. [10] F. Schottky: Über eine spezielle Function, welche bei einer bestimmten linearen Transformation ihres Arguments unverändert bleibt, J. Reine Angew. Math.101 (1887), 227-272. JFM19.0424.02

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.