On the varieties defined by Riemann-Mumford’s relations
HTML articles powered by AMS MathViewer
- by Riccardo Salvati Manni PDF
- Proc. Amer. Math. Soc. 135 (2007), 1241-1247 Request permission
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
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157, DOI 10.1007/978-1-4757-3849-0
- Jun-ichi Igusa, Theta functions, Die Grundlehren der mathematischen Wissenschaften, Band 194, Springer-Verlag, New York-Heidelberg, 1972. MR 0325625, DOI 10.1007/978-3-642-65315-5
- George R. Kempf, Linear systems on abelian varieties, Amer. J. Math. 111 (1989), no. 1, 65–94. MR 980300, DOI 10.2307/2374480
- Herbert Lange and Christina Birkenhake, Complex abelian varieties, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 302, Springer-Verlag, Berlin, 1992. MR 1217487, DOI 10.1007/978-3-662-02788-2
- Toshitsune Miyake, Modular forms, Springer-Verlag, Berlin, 1989. Translated from the Japanese by Yoshitaka Maeda. MR 1021004, DOI 10.1007/3-540-29593-3
- D. Mumford, On the equations defining abelian varieties. I, Invent. Math. 1 (1966), 287–354. MR 204427, DOI 10.1007/BF01389737
- David Mumford, Tata lectures on theta. III, Progress in Mathematics, vol. 97, Birkhäuser Boston, Inc., Boston, MA, 1991. With the collaboration of Madhav Nori and Peter Norman. MR 1116553, DOI 10.1007/978-0-8176-4579-3
- Riccardo Salvati Manni, On the projective varieties associated with some subrings of the ring of Thetanullwerte, Nagoya Math. J. 133 (1994), 71–83. MR 1266363, DOI 10.1017/S002776300000475X
- Riccardo Salvati Manni, Modular varieties with level $2$ theta structure, Amer. J. Math. 116 (1994), no. 6, 1489–1511. MR 1305875, DOI 10.2307/2375056
- R. Salvati Manni, On the differential of applications defined on moduli spaces of p.p.a.v. with level theta structure, Math. Z. 221 (1996), no. 2, 231–241. MR 1376295, DOI 10.1007/BF02622113
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
- Received by editor(s): November 14, 2004
- Received by editor(s) in revised form: November 20, 2005
- Published electronically: October 18, 2006
- Communicated by: Michael Stillman
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1241-1247
- MSC (2000): Primary 11F46
- DOI: https://doi.org/10.1090/S0002-9939-06-08635-7
- MathSciNet review: 2276630