The Kodaira dimension of Siegel modular varieties of genus 3 or higher

Eric Schellhammer

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 749-776
  • ISSN: 0392-4033

Abstract

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We consider the moduli space A pol ( n ) of (non-principally) polarised abelian varieties of genus g 3 with coprime polarisation and full level-n structure. Based upon the analysis of the Tits building in [S], we give an explicit lower bound on n that is sufficient for the compactified moduli space to be of general type if one further explicit condition is satisfied.

How to cite

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Schellhammer, Eric. "The Kodaira dimension of Siegel modular varieties of genus 3 or higher." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 749-776. <http://eudml.org/doc/289637>.

@article{Schellhammer2006,
abstract = {We consider the moduli space $A_\{\text\{pol\}\}(n)$ of (non-principally) polarised abelian varieties of genus $g \geq 3$ with coprime polarisation and full level-n structure. Based upon the analysis of the Tits building in [S], we give an explicit lower bound on n that is sufficient for the compactified moduli space to be of general type if one further explicit condition is satisfied.},
author = {Schellhammer, Eric},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {749-776},
publisher = {Unione Matematica Italiana},
title = {The Kodaira dimension of Siegel modular varieties of genus 3 or higher},
url = {http://eudml.org/doc/289637},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Schellhammer, Eric
TI - The Kodaira dimension of Siegel modular varieties of genus 3 or higher
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 749
EP - 776
AB - We consider the moduli space $A_{\text{pol}}(n)$ of (non-principally) polarised abelian varieties of genus $g \geq 3$ with coprime polarisation and full level-n structure. Based upon the analysis of the Tits building in [S], we give an explicit lower bound on n that is sufficient for the compactified moduli space to be of general type if one further explicit condition is satisfied.
LA - eng
UR - http://eudml.org/doc/289637
ER -

References

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  1. ASH, A. - MUMFORD, D. - RAPOPORT, M. - TAI, Y., Smooth Compactification of Locally Symmetric Varieties, Brookline: Math. Sci Press1975. Zbl0334.14007
  2. BRASCH, H.-J., Lifting level D-structures of abelian varieties, Arch. Math., Vol. 60 (1993), 553-562. Zbl0787.14025
  3. BARNES, E. S. - COHN, M. J., On the inner product of positive quadratic forms, J. London Math. Soc. (2), 12 (1975), 32-36. Zbl0312.10013
  4. BIRKENHAKE, C. - LANGE, H., An isomorphism between moduli spaces of abelian varieties, Math. Nach., Vol. 253, Iss. 1 (2003), 3-7. Zbl1034.14019
  5. CASSELS, J. W. S., An introduction to the geometry of numbers, Springer-Verlag, 1959. Zbl0086.26203
  6. FREITAG, E., Siegelsche Modulfunktionen, Springer-Verlag, 1983. 
  7. HULEK, K., Igusa's Modular Form and the Classification of Siegel Modular Threefolds, Moduli of Abelian Varieties. Progress in Mathematics195, Birkhauser Verlag (2001), 217-229. Zbl1054.14027
  8. HULEK, K. - KAHN, C. - WEINTRAUB, S. H., Moduli Spaces of Abelian Surfaces: Compactification, Degenerations and Theta Functions, De Gruyter Expositions in Mathematics12, 1993. Zbl0809.14035
  9. HULEK, K. - SANKARAN, G. K., The Geometry of Siegel Modular Varieties, Advanced Studies in Pure Mathematics35 (2002), Higher Dimensional Birational Geometry, 89-156. Zbl1074.14021
  10. MUMFORD, D., Hirzebruch's Proportionality Theorem in the Non-Compact Case, Inv. Math., 42 (1977), 239-272. Zbl0365.14012
  11. MUMFORD, D., On the Kodaira Dimension of the Siegel Modular Variety, Lec. Notes in Math. Vol. 997, Springer-Verlag, 1983, 348-376. Zbl0527.14036
  12. NAMIKAWA, Y., Toroidal Compactification of Siegel Spaces, Lec. Notes in Math. Vol. 812, Springer-Verlag, 1980. Zbl0466.14011
  13. NATHANSON, M. B., Elementary Methods in Number Theory, Springer-Verlag, 1991. 
  14. ODA, T., Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties, Ergeb. Math. Grenzgeb., 3 Folge, 15 (1988), Berlin, Springer-Verlag. Zbl0628.52002
  15. SCHELLHAMMER, E., On the Tits building of paramodular groupshttp://arXiv.org/abs/math/0405321 Zbl1177.51011
  16. TAI, Y.-S., On the Kodaira Dimension of the Moduli Space of Abelian Varieties, Invent. Math., 68 (1982), 425-439. Zbl0508.14038
  17. TAI, Y.-S., On the Kodaira Dimension of the Moduli Spaces of Abelian Varieties with non-principal polarizations, In: Abelian Varietes, Egloffstein 1993, 293-302, de Gruyter, 1995. Zbl0848.14021

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