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On the varieties defined by Riemann-Mumford's relations
Author(s):
Riccardo
Salvati Manni
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1241-1247.
MSC (2000):
Primary 11F46
Posted:
October 18, 2006
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Abstract:
In this paper we consider varieties defined by Riemann-Mumford's relations. An irreducible component of these varieties is related to Siegel modular varieties. We prove that in most cases Riemann-Mumford varieties are not irreducible.
References:
-
- 1.
- Hartshorne,R.: Algebraic geometry. Graduate Texts in Mathematics, 52 xvi+496 pp., Springer-Verlag, New York-Heidelberg, 1977. MR 0463157 (57:3116)
- 2.
- Igusa, J.: Theta Functions. Grundlehren der mathematischen Wissenschaften, 194. Berlin-Heidelberg-New York: Springer (1972). MR 0325625 (48:3972)
- 3.
- Kempf, G.: Linear systems on abelian varieties. Amer. J. Math. 111 , 65-94 (1989). MR 0980300 (90d:14046)
- 4.
- Lange, H., Birkenhake, C.: Complex Abelian Varieties. Grundlehren der mathematischen Wissenschaften, 302. Berlin-Heidelberg-New York: Springer (1992). MR 1217487 (94j:14001)
- 5.
- Miyake, T.: Modular forms. Translated from the Japanese by Yoshitaka Maeda , x+335 pp. Springer-Verlag, Berlin, (1989). MR 1021004 (90m:11062)
- 6.
- Mumford, D.: On the Equations Defining Abelian Varieties I, II, III. Invent. Math. 1 287-354 (1966), 3 71-135, 215-244 (1967). MR 0204427 (34:4269); MR 0219541 (36:2621); MR 0219542 (36:2622)
- 7.
- Mumford, D.: Tata Lectures on Theta III. Progress in Mathematics, 97. Boston-Basel-Berlin: Birkhäuser (1991). MR 1116553 (93d:14065)
- 8.
- Salvati Manni, R.: On the Projective Varieties Associated with some Subrings of the Ring of Thetanullwerte. Nagoya Math. J. 133 , 71-83 (1994). MR 1266363 (95f:14088)
- 9.
- Salvati Manni, R.: Modular varieties with level 2 theta structure. Amer. J. Math. 111 , 1489-1511 (1994). MR 1305875 (96c:11051)
- 10.
- Salvati Manni, R.: On the differential of applications defined on the moduli spaces of p.p.a.v. with level theta structure. Math.Z. 221 , 231-241 (1996). MR 1376295 (96k:11059)
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Additional Information:
Riccardo
Salvati Manni
Affiliation:
Dipartimento di Matematica, Università di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185 Roma, Italy
Email:
salvati@mat.uniroma1.it
DOI:
10.1090/S0002-9939-06-08635-7
PII:
S 0002-9939(06)08635-7
Received by editor(s):
November 14, 2004
Received by editor(s) in revised form:
November 20, 2005
Posted:
October 18, 2006
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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