Schellhammer, Eric:
The Kodaira dimension of Siegel modular varieties of genus 3 or higher
Bollettino dell'Unione Matematica Italiana Serie 8 9-B (2006), fasc. n.3, p. 749-776, (English)
pdf (478 Kb), djvu (278 Kb). | MR 2274125 | Zbl 1182.14017
Sunto
Consideriamo lo spazio dei moduli $A_{\text{pol}}(n)$ delle varietà abeliane (non principalmente) polarizzate di genere $g \geq 3$ con polarizzazione coprima e struttura di livello n completa. Basandoci sull'analisi dei building di Tits di [S], diamo un limite inferiore esplicito per n che è sufficiente affinché lo spazio dei moduli compattificato sia di tipo generale, se un'ulteriore condizione esplicita viene soddisfatta.
Referenze Bibliografiche
[AMRT]
A. ASH -
D. MUMFORD -
M. RAPOPORT -
Y. TAI,
Smooth Compactification of Locally Symmetric Varieties, Brookline:
Math. Sci Press 1975. |
Zbl 0334.14007[B]
H.-J. BRASCH,
Lifting level D-structures of abelian varieties,
Arch. Math., Vol.
60 (
1993), 553-562. |
Zbl 0787.14025[BC]
E. S. BARNES -
M. J. COHN,
On the inner product of positive quadratic forms,
J. London Math. Soc. (2),
12 (
1975), 32-36. |
Zbl 0312.10013[BL]
C. BIRKENHAKE -
H. LANGE,
An isomorphism between moduli spaces of abelian varieties,
Math. Nach., Vol.
253, Iss. 1 (
2003), 3-7. |
Zbl 1034.14019[C]
J. W. S. CASSELS,
An introduction to the geometry of numbers,
Springer-Verlag,
1959. |
Zbl 0086.26203[F] E. FREITAG, Siegelsche Modulfunktionen, Springer-Verlag, 1983.
[H]
K. HULEK,
Igusa's Modular Form and the Classification of Siegel Modular Threefolds,
Moduli of Abelian Varieties.
Progress in Mathematics 195,
Birkhauser Verlag (
2001), 217-229. |
Zbl 1054.14027[HKW]
K. HULEK -
C. KAHN -
S. H. WEINTRAUB,
Moduli Spaces of Abelian Surfaces: Compactification, Degenerations and Theta Functions,
De Gruyter Expositions in Mathematics 12,
1993. |
Zbl 0809.14035[HS]
K. HULEK -
G. K. SANKARAN,
The Geometry of Siegel Modular Varieties,
Advanced Studies in Pure Mathematics 35 (
2002),
Higher Dimensional Birational Geometry, 89-156. |
Zbl 1074.14021[M]
D. MUMFORD,
Hirzebruch's Proportionality Theorem in the Non-Compact Case,
Inv. Math.,
42 (
1977), 239-272. |
fulltext EuDML |
Zbl 0365.14012[M2]
D. MUMFORD,
On the Kodaira Dimension of the Siegel Modular Variety,
Lec. Notes in Math. Vol.
997,
Springer-Verlag,
1983, 348-376. |
Zbl 0527.14036[Nami]
Y. NAMIKAWA,
Toroidal Compactification of Siegel Spaces,
Lec. Notes in Math. Vol.
812,
Springer-Verlag,
1980. |
Zbl 0466.14011[Nath] M. B. NATHANSON, Elementary Methods in Number Theory, Springer-Verlag, 1991.
[O]
T. ODA,
Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties,
Ergeb. Math. Grenzgeb., 3 Folge,
15 (
1988), Berlin,
Springer-Verlag. |
fulltext EuDML |
Zbl 0628.52002[S]
E. SCHELLHAMMER,
On the Tits building of paramodular groups http://arXiv.org/abs/math/0405321 |
Zbl 1177.51011[T]
Y.-S. TAI,
On the Kodaira Dimension of the Moduli Space of Abelian Varieties,
Invent. Math.,
68 (
1982), 425-439. |
fulltext EuDML |
Zbl 0508.14038[T2]
Y.-S. TAI,
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. |
Zbl 0848.14021
Con il contributo del Ministero per i Beni e le Attività Culturali