On Mumford's construction of degenerating abelian varieties
Valery Alexeev and Iku Nakamura
Source: Tohoku Math. J. (2) Volume 51, Number 3
(1999), 399-420.
First Page:
Show
Hide
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.tmj/1178224770
Mathematical Reviews number (MathSciNet): MR1707764
Zentralblatt MATH identifier: 0989.14003
Digital Object Identifier: doi:10.2748/tmj/1178224770
References
[Ale] V ALEXEEV, Complete moduli in the presence of semiabelian group action, in preparation
[AW71] M ARTIN AND G WINTERS, Degenerate fibers and stable reduction of curves, Topology 10 (1971), 373-383
Mathematical Reviews (MathSciNet): MR476756
Zentralblatt MATH: 0196.24403
Digital Object Identifier: doi:10.1016/0040-9383(71)90028-0
[Cha85] C. -L CHAI, Compactification of Siegel moduli schemes, London Math Soc. Lecture Note Ser, vo 107, Cambridge Univ Press, 1985
Mathematical Reviews (MathSciNet): MR853543
Zentralblatt MATH: 0578.14009
[CS93] J H CONWAY AND N J A SLOANE, Sphere packings, lattices and groups, 2nd ed, Grundlehre Math. Wiss, vol 290, Springer-Verlag, 1993
Mathematical Reviews (MathSciNet): MR1194619
Zentralblatt MATH: 0785.11036
[ER87] R M ERDAHL AND S S RYSHKOV, The empty sphere, I, Canad J Math 39 (1987), New York, 794-824
Mathematical Reviews (MathSciNet): MR915016
Zentralblatt MATH: 0643.10025
[Erd92] R. M ERDAHL, A cone of inhomogeneous second-order polynomials, Discrete Comput Geom (1992), 387-415
Mathematical Reviews (MathSciNet): MR1176378
Zentralblatt MATH: 0773.11042
[Fal85] G FALTINGS, Arithmetische Kompaktifizierung des Modulraums der Abelischen Varieetaten, Lectur Notes in Math (1985), Springer-Verlag, no. 1111, 321-383
Mathematical Reviews (MathSciNet): MR797429
Zentralblatt MATH: 0597.14036
[FC90] G FALTINGS AND C -L CHAI, Degenerations of abelian varieties, vol 22, Ergeb Math Grenzgeb, Springer-Verlag, 1990
Mathematical Reviews (MathSciNet): MR1083353
Zentralblatt MATH: 0744.14031
[Har77] R HARTSHORNE, Algebraic geometry, Grad Texts in Math, vol 52, Springer-Verlag, 197
Mathematical Reviews (MathSciNet): MR463157
Zentralblatt MATH: 0367.14001
[Mat89] H MATSUMURA, Commutative ring theory, Cambridge Stud Adv Math, vol 8, Cambridge Uni Press, Cambridge-New York, 1989.
Mathematical Reviews (MathSciNet): MR1011461
Zentralblatt MATH: 0603.13001
[Mum72] D MUMFORD, An analytic constructionof degenerating abelian varieties over complete rings, Compo sitio Math 24 (1972), no 3, 239-272
Mathematical Reviews (MathSciNet): MR352106
Zentralblatt MATH: 0241.14020
[Mum83] D MUMFORD, On the Kodaira dimension of the Siegel modular variety, Algebraic geometry--ope problems (Ravello, 1982), 348-375, Lecture Notes in Math, 997, Springer, Berlin-New York, 1983
Mathematical Reviews (MathSciNet): MR714757
Zentralblatt MATH: 0527.14036
Digital Object Identifier: doi:10.1007/BFb0061652
[Nak75] I. NAKAMURA, On moduli of stable quasi abelian varieties, Nagoya Math J 58 (1975), 149-21
Mathematical Reviews (MathSciNet): MR393049
Zentralblatt MATH: 0295.14018
Project Euclid: euclid.nmj/1118795447
[Nak77] I NAKAMURA, Relative compactification of the Neron model and its applications, Complex Analysi and Algebraic Geometry (W L Baily, Jr and T Shioda, eds), Cambridge Univ Press, Cambridge-New York, 1977, pp 207-225
Mathematical Reviews (MathSciNet): MR457435
Zentralblatt MATH: 0365.14005
Digital Object Identifier: doi:10.1017/CBO9780511569197.016
[Nam76] Y NAMIKAWA, A new compactification of the Siegel space and degenerations of abelian varieties, I, II, Math Ann 221 (1976), 97-141, 201-241
Mathematical Reviews (MathSciNet): MR480537
Zentralblatt MATH: 0306.14016
Digital Object Identifier: doi:10.1007/BF01433145
[Nam77] Y NAMIKAWA, Toroidal degeneration of Abelian varieties, Complex Analysis and Algebraic Geometr (W L Baily, Jr and T Shioda, eds), Cambridge Univ Press, Cambridge-New York, 1977, pp. 227-239
Mathematical Reviews (MathSciNet): MR457436
Zentralblatt MATH: 0351.14020
Digital Object Identifier: doi:10.1017/CBO9780511569197.017
[Nam79] Y NAMIKAWA, Toroidal degeneration of abelian varieties II, Math. Ann 245 (1979), 117-15
Mathematical Reviews (MathSciNet): MR552583
Zentralblatt MATH: 0405.14020
Digital Object Identifier: doi:10.1007/BF01428801
[NamSO] Y NAMIKAWA, Toroidal compactificationof Siegel spaces, Lecture Notes in Math, vol 812, Springer Verlag, 1980
Mathematical Reviews (MathSciNet): MR584625
Zentralblatt MATH: 0466.14011
[OBS92] A OKABE, B. BOOTS, AND K. SUGIHARA, Spatial tesselations: concepts and applications of Vorono diagrams, Wiley Ser Probab Math Statist: Applied Probability and Statistics, John Wiley and Sons, Ltd, Chichester, 1992
Mathematical Reviews (MathSciNet): MR1210959
Zentralblatt MATH: 0877.52010
[Oda88] T ODA, Convex bodies and algebraic geometry, vol. 15, Ergeb. Math. Grenzgeb., Springer-Verlag, 198
Mathematical Reviews (MathSciNet): MR922894
Zentralblatt MATH: 0628.52002
[Ser79] J -P. SERRE, Local fields, Grad Texts in Math, vol 67, Springer-Verlag, 197
Mathematical Reviews (MathSciNet): MR554237
Zentralblatt MATH: 0423.12016
[SGA7 1] A GROTHENDIECK, M RAYNAUD, AND D. S RIM, SGA7 I. Groupes de monodromie en geometri algebrique, Lecture Notes in Math., vol 288, Springer-Verlag, 1972.
Mathematical Reviews (MathSciNet): MR354656
[TE73] G KEMPF, F KNUDSEN, D. MUMFORD, AND B. SAINT-DONAT, Toroidal embeddings I, Lectur Notes in Math., vol.339, Springer-Verlag, 1973.
Mathematical Reviews (MathSciNet): MR335518
Zentralblatt MATH: 0271.14017
[Vor09] G. VORONOI, Nouvelles applications des parametres continus a la theorie des formes quadratique, I, II, III, J ReineAngew Math 133, 134, 136(1908, 1909), 97-178, 198-287, 67-181
Tohoku Mathematical Journal
