A Siegel modular 3-fold that is a Picard modular 3-fold

Bruce Hunt

Compositio Mathematica (1990)

  • Volume: 76, Issue: 1-2, page 203-242
  • ISSN: 0010-437X

How to cite

top

Hunt, Bruce. "A Siegel modular 3-fold that is a Picard modular 3-fold." Compositio Mathematica 76.1-2 (1990): 203-242. <http://eudml.org/doc/90047>.

@article{Hunt1990,
author = {Hunt, Bruce},
journal = {Compositio Mathematica},
keywords = {Siegel modular three-fold; Humbert surfaces; Picard modular three-folds; theta constants; Tits buildings; hypergeometric differential equations},
language = {eng},
number = {1-2},
pages = {203-242},
publisher = {Kluwer Academic Publishers},
title = {A Siegel modular 3-fold that is a Picard modular 3-fold},
url = {http://eudml.org/doc/90047},
volume = {76},
year = {1990},
}

TY - JOUR
AU - Hunt, Bruce
TI - A Siegel modular 3-fold that is a Picard modular 3-fold
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 76
IS - 1-2
SP - 203
EP - 242
LA - eng
KW - Siegel modular three-fold; Humbert surfaces; Picard modular three-folds; theta constants; Tits buildings; hypergeometric differential equations
UR - http://eudml.org/doc/90047
ER -

References

top
  1. [B] Baker, H.F., Principles of Geometry, Vol. IV, Ch. 5, Cambridge University Press, London, 1940. 
  2. [C] Christian, U., Über die Modulgruppe zweiten grades I, Math. Zeit.85, (1964) 1-28. Zbl0143.30404MR168807
  3. [DM] Deligne, P. and Mostow, G., Monodromy of hypergeometric functions and non-integral lattice monodromy, Pupl. Math. IHES, 63 (1986) 113-140. Zbl0615.22008
  4. [F] Feustel, J.M., Ringe automorpher Formen auf der komplexen Einheitskugel und ihre Erzeugung durch Theta-Konstanten. Preprint P-Math-13/86, Akademie der Wissenschaften, Berlin. 
  5. [GHv] Gerritzen, L., Herrlich, F. and van der Put, M., Stable n-pointed trees of projective lines. To appear in Indagationes. Zbl0698.14019
  6. [Gr] Griffiths, P., Periods of integrals on algebraic manifolds. Bull. AMS76, (1970) 228-296. Zbl0214.19802MR258824
  7. [GS] Griffiths, P. and Schmid, W., Locally homogenous complex manifolds. Acta Math.123 (1969) 253-302. Zbl0209.25701MR259958
  8. [HK] Hashimoto, K. and Koseki, H., On class numbers of positive definite binary and ternary unimodular hermitian forms. Math. Gottingensis (1987) 21-22. Zbl0617.10018
  9. [He] Hemperly, J.C., The parabolic contribution to the number of linearly independent automorphic forms on a certain bounded domain. Amer. J. Math., 94 (1972) 1078-1100. Zbl0259.32010MR407334
  10. [Hi] Hirzebruch, F., Automorphe Formen und der Satz von Riemann Roch. in: Symp. Inter. de Top. Alg., Unesco1958. Zbl0129.29801MR103280
  11. [Ho1] Holzapfel, R.-P., Geometry and Arithmetic around Euler partial differential equations. D. Reidel Publishing Company: Boston1986. Zbl0595.14016MR867406
  12. [Ho2] Holzapfel, R.-P., On the nebentypus of Picard modular forms. To appear in Math. Nach. Zbl0696.10022MR978113
  13. [HSY] Hara, M., Sasaki, T. and Yoshida, M., Tensor products of Linear Differential Equations. Preprint Kyushu University. 
  14. [Hu] Hunt, B., Coverings and Ball Quotients. Bonn. Math. Schrif.174, Bonn, 1986. Zbl0613.14032MR865805
  15. [I1] Igusa, J., On Siegel modular forms of genus two. Am. J. Math.84 (1962) 175-200 and 86 (1964) 392-412. Zbl0133.33301MR141643
  16. [I2] Igusa, J., On the graded ring of Theta Constants. Am. J. Math.86 (1964) 219-246 and 88 (1966) 221-236. Zbl0146.31704MR164967
  17. [I3] Igusa, J., On a desingularisation problem in the theory of Siegel modular forms. Math. Ann.168 (1967) 228-260. Zbl0145.09702MR218352
  18. [Ka] Katz, N., On the differential equations satisfied by period matrices. Publ. Math. IHES35, 71-106 (1968) Zbl0159.22502MR242841
  19. [KLW] Kirwan, F., Lee, R. and Weintraub, S., Quotients of the complex ball by discrete groups. Pac. J. Math.130, (1987) 115-141. Zbl0597.57023MR910656
  20. [K] Kodaira, K., On Kähler varieties of restricted type. Ann. of Math.60, (1954) 28-48. Zbl0057.14102MR68871
  21. [LW] Lee, R. and Weintraub, S., Cohomology of Sp4(Z) and related groups and spaces. Topology, 24, (1985) 391-410. Zbl0601.22005MR816521
  22. [LW1] Lee, R. and Weintraub, S., Moduli spaces of Riemann surfaces of genus two with level structures. I. Math. Gottingensis.66 (1986), to appear in Trans. AMS, 1988. Zbl0601.14021MR965750
  23. [OS] Orlik, P. and Solomon, L.: Arrangements defined by unitary reflection groups., Math. Ann.261, (1982) 339-357. Zbl0491.51018MR679795
  24. [P] Picard, E., Sur les fonctions hyperfuchsiennes provenant des series hypergeometriques de deux variables. Ann. Ecole Norm. Sup.3e ser. 62, (1885) 357-384. MR1508769JFM17.0412.01
  25. [SH] Schmickler-Hirzebruch, U., Elliptische Flächen über P1 mit drei Ausnahmefasern und die hypergeometrische Differentialgleichung. Diplomarbeit, Bonn, 1978. 
  26. [S] Shimura, G., On purely transcendental fields of automorphic functions of several variables. Osaka J. Math.1, (1964) 1-14. Zbl0149.04302MR176113
  27. [St] Stiller, P., The differential equation associated with elliptic surfaces. J. Math. Soc. Japan24, (1972) 20-59. Zbl0476.14014MR607940
  28. [T] Terada, T., Fonctions hypergeometriques F1 et fonctions automorphes I. J. Math. Soc. Japan35, (1983) 451-475. Zbl0506.33001MR702770
  29. [V] van der Geer, G., On the geometry of a Siegel modular threefold. Math. Ann.260, (1982) 317-350. Zbl0473.14017MR669299
  30. [Y] Yoshida, M., Fuchsian differential equations. Viehweg, Braunschweig/Wiesbaden1987 Zbl0618.35001MR986252
  31. [Z] Zeltinger, H., Volumina und Spitzenanzahlen Picardscher Modulvarietaeten. Bonn. Math. Schrif.136, (1981). Zbl0501.10027MR645358

NotesEmbed ?

top

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.