On the Tits building of paramodular groups

Eric Schellhammer

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 619-643
  • ISSN: 0392-4033

Abstract

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We investigate the Tits buildings of the paramodular groups with or without canonical level structure, respectively. These give important combinatorical information about the boundary of the toroidal compactification of the moduli spaces of non-principally polarised Abelian varieties. We give a full classification of the isotropic lines for all of these groups. Furthermore, for square-free, coprime polarisations without level structure we show that there is only one top-dimensional isotropic subspace. In a sequel to this paper we will use this information to establish a general type result for the moduli space of non-principally polarised Abelian varieties with full level structure.

How to cite

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Schellhammer, Eric. "On the Tits building of paramodular groups." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 619-643. <http://eudml.org/doc/289634>.

@article{Schellhammer2006,
abstract = {We investigate the Tits buildings of the paramodular groups with or without canonical level structure, respectively. These give important combinatorical information about the boundary of the toroidal compactification of the moduli spaces of non-principally polarised Abelian varieties. We give a full classification of the isotropic lines for all of these groups. Furthermore, for square-free, coprime polarisations without level structure we show that there is only one top-dimensional isotropic subspace. In a sequel to this paper we will use this information to establish a general type result for the moduli space of non-principally polarised Abelian varieties with full level structure.},
author = {Schellhammer, Eric},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {619-643},
publisher = {Unione Matematica Italiana},
title = {On the Tits building of paramodular groups},
url = {http://eudml.org/doc/289634},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Schellhammer, Eric
TI - On the Tits building of paramodular groups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 619
EP - 643
AB - We investigate the Tits buildings of the paramodular groups with or without canonical level structure, respectively. These give important combinatorical information about the boundary of the toroidal compactification of the moduli spaces of non-principally polarised Abelian varieties. We give a full classification of the isotropic lines for all of these groups. Furthermore, for square-free, coprime polarisations without level structure we show that there is only one top-dimensional isotropic subspace. In a sequel to this paper we will use this information to establish a general type result for the moduli space of non-principally polarised Abelian varieties with full level structure.
LA - eng
UR - http://eudml.org/doc/289634
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. FRIEDLAND, M. - SANKARAN, G. K., Das Titsgebäude von Siegelschen Modulgruppen vom Geschlecht 2, Abh. Math. Sem. Univ. Hamburg71 (2001), 49-68. 
  3. 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
  4. OELJEKLAUS, E. - REMMERT, R., Lineare Algebra I, Springer-Verlag, 1974. 

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