The Kodaira dimension of certain moduli spaces of abelian surfaces

K. Hulek; G. K. Sankaran

Compositio Mathematica (1994)

  • Volume: 90, Issue: 1, page 1-35
  • ISSN: 0010-437X

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Hulek, K., and Sankaran, G. K.. "The Kodaira dimension of certain moduli spaces of abelian surfaces." Compositio Mathematica 90.1 (1994): 1-35. <http://eudml.org/doc/90265>.

@article{Hulek1994,
author = {Hulek, K., Sankaran, G. K.},
journal = {Compositio Mathematica},
keywords = {Kodaira dimension; surface of general type; moduli space of complex abelian varieties; principal polarization},
language = {eng},
number = {1},
pages = {1-35},
publisher = {Kluwer Academic Publishers},
title = {The Kodaira dimension of certain moduli spaces of abelian surfaces},
url = {http://eudml.org/doc/90265},
volume = {90},
year = {1994},
}

TY - JOUR
AU - Hulek, K.
AU - Sankaran, G. K.
TI - The Kodaira dimension of certain moduli spaces of abelian surfaces
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 90
IS - 1
SP - 1
EP - 35
LA - eng
KW - Kodaira dimension; surface of general type; moduli space of complex abelian varieties; principal polarization
UR - http://eudml.org/doc/90265
ER -

References

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  1. [Ba] W.L. Baily: Fourier-Jacobi Series. In: Proc. Symp. Pure Math. IX, AMS, Providence, R.I., (1966), 296-300. Zbl0164.38501MR219755
  2. [BH] W. Barth, K. Hulek: Projective models of Shioda modular surfaces. Manuscr. Math.50 (1985), 73-132. Zbl0599.14035MR784140
  3. [EZ] M. Eichler, D. Zagier: The theory of Jacobi forms. Progress in Mathematics 55. Birkhäuser, Boston, Basel, Stuttgart1985. Zbl0554.10018MR781735
  4. [F] E. Freitag: Siegelsche Modulfunktionen. Grundlehren254, Springer, Berlin1983. Zbl0498.10016MR871067
  5. [Fu] W. Fulton: Intersection theory. Springer, Berlin1984. Zbl0541.14005MR732620
  6. [H] R. Hartshorne: Algebraic geometry. Springer, New York, 1977. Zbl0367.14001MR463157
  7. [Hir] F. Hirzebruch: Elliptische Differentialoperatoren auf Mannigfaltigkeiten. Gesammelte Werke Vol. 2, 583-608. Springer, Berlin, 1987. MR210151
  8. [HM] G. Horrocks, D. Mumford: A rank 2 vector bundle on P4 with 15,000 symmetries. Topology12 (1973), 69-85. Zbl0255.14017MR382279
  9. [HKW1] K. Hulek, C. Kahn, S.H. Weintraub: Singularities of the moduli spaces of certain abelian surfaces. Compositio Math.79 (1991), 231-253. Zbl0741.14022MR1117341
  10. [HKW2] K. Hulek, C. Kahn, S.H. Weintraub: Moduli spaces of abelian surfaces: Compactification, degenerations and theta functions. de Gruyter, Berlin1993. Zbl0809.14035MR1257185
  11. [HW] K. Hulek, S.H. Weintraub: Bielliptic abelian surfaces. Math. Ann.283 (1989), 411-429. Zbl0641.14014MR985240
  12. [K] J. Kramer: A geometrical approach to the theory of Jacobi forms. Compositio Math.79 (1991), 1-19. Zbl0724.11028MR1112278
  13. [M1] D. Mumford: Hirzebruch's proportionality theorem in the non-compact case. Inv. Math.42 (1977), 239-272. Zbl0365.14012MR471627
  14. [M2] D. Mumford: On the Kodaira dimension of the Siegel modular variety. Algebraic Geometry-Open Problems, Proceedings Ravello1982, 348-375 (C. Ciliberto et al., Eds) Springer Lecture Notes997, Springer, Berlin, 1983. Zbl0527.14036MR714757
  15. [O'G] K O'Grady: On the Kodaira dimension of moduli spaces of abelian surfaces. Compositio Math.72 (1989), 121-163. Zbl0711.14025MR1030139
  16. [Sch] B. Schoeneberg: Elliptic modular functions. Grundlehren203, Springer, Berlin, 1974. Zbl0285.10016MR412107
  17. [Sh] G. Shimura: Introduction to the arithmetic theory of automorphic functions. Publ. Math. Soc. Japan 11, Iwanami Shoten, Tokyo, and Princeton University Press, 1971. Zbl0221.10029MR314766
  18. [Shi] T. Shioda: On elliptic modular surfaces. J. Math. Soc. Japan24 (1972), 20-59. Zbl0226.14013MR429918
  19. [SC] A. Ash, D. Mumford, M. Rapoport, Y. Tai: Smooth compactification of locally symmetric varieties. Math. Sci. Press, Brookline, Mass., 1975. Zbl0334.14007MR457437
  20. [T] Y. Tai: On the Kodaira dimension of the moduli spaces of abelian varieties. Inv. Math.68 (1982), 425-439. Zbl0508.14038MR669424
  21. [YPG] M. Reid: Young person's guide to canonical singularities. Proc. Symp. Pure Math. 46 (Algebraic Geometry Bowdoin 1985), 345-416 (1987). Zbl0634.14003MR927963

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