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: 0392-4041

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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  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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