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On the graded ring of modular forms of the siegel paramodular group of level 2

On the graded ring of modular forms of the siegel paramodular group of level 2 Abh. Math. Sem. Univ. Hamburg 67 (1997), 297-305 On the Graded Ring of Modular Forms of the Siegel Paramodular Group of Level 2 By T. IBUKIYAMA and E ONODERA In this paper, we shall describe the concrete ring structure of the graded rings of modular forms belonging to the Siegel paramodular group Fpara(2) of degree two with polarization diag(1,2). We also show that the Satake compactification of the quotient variety by this group is rational. Here, for each prime p, we define the group Fpa~(p) by rPara(p) := {g E M4(Z) [ tgJ2(P)g = J2(P)}, where for any number d, we put 0 0 J2(d) = 0 0 " (11~ i) -d 0 The main results will be given in Section 1. Historically, FREITAG [1] has obtained the ring structure for a certain group which contains our group Fpara(2) with index 2. He used some geometri- cal method. Since the dimension formula for l"para(p) has been known by IBUKIYAMA [9], we can use more direct method here, and his result is also obtained as a corollary of our result. Various generators of the ring have been considered by various approach (cf. GRITSENKO [2], [3], GRITSENKO and NIKULIN [4], [5], http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

On the graded ring of modular forms of the siegel paramodular group of level 2

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References (15)

Publisher
Springer Journals
Copyright
Copyright © 1997 by Mathematische Seminar
Subject
Mathematics; Algebra; Differential Geometry; Combinatorics; Number Theory; Topology; Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/BF02940837
Publisher site
See Article on Publisher Site

Abstract

Abh. Math. Sem. Univ. Hamburg 67 (1997), 297-305 On the Graded Ring of Modular Forms of the Siegel Paramodular Group of Level 2 By T. IBUKIYAMA and E ONODERA In this paper, we shall describe the concrete ring structure of the graded rings of modular forms belonging to the Siegel paramodular group Fpara(2) of degree two with polarization diag(1,2). We also show that the Satake compactification of the quotient variety by this group is rational. Here, for each prime p, we define the group Fpa~(p) by rPara(p) := {g E M4(Z) [ tgJ2(P)g = J2(P)}, where for any number d, we put 0 0 J2(d) = 0 0 " (11~ i) -d 0 The main results will be given in Section 1. Historically, FREITAG [1] has obtained the ring structure for a certain group which contains our group Fpara(2) with index 2. He used some geometri- cal method. Since the dimension formula for l"para(p) has been known by IBUKIYAMA [9], we can use more direct method here, and his result is also obtained as a corollary of our result. Various generators of the ring have been considered by various approach (cf. GRITSENKO [2], [3], GRITSENKO and NIKULIN [4], [5],

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals

Published: Aug 27, 2008

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