論文

査読有り
2017年

On some Siegel threefold related to the tangent cone of the Fermat quartic surface

Advances in Theoretical and Mathematical Physics
  • Takeo Okazaki
  • ,
  • Takuya Yamauchi

21
3
開始ページ
585
終了ページ
630
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.4310/ATMP.2017.v21.n3.a1
出版者・発行元
International Press of Boston, Inc.

Let Z be the quotient of the Siegel modular threefold Asa(2, 4, 8) which has been studied by van Geemen and Nygaard. They gave an implication that some 6-tuple FZ of theta constants which is in turn known to be a Klingen type Eisenstein series of weight 3 should be related to a holomorphic differential (2, 0)-form on Z. The variety Z is birationally equivalent to the tangent cone of Fermat quartic surface in the title. In this paper we first compute the L-function of two smooth resolutions of Z. One of these, denoted by W, is a kind of Igusa compactification such that the boundary ∂W is a strictly normal crossing divisor. The main part of the L-function is described by some elliptic newform g of weight 3. Then we construct an automorphic representation π of GSp2(A) related to g and an explicit vector EZ sits inside π which creates a vector valued (non-cuspidal) Siegel modular form of weight (3, 1) so that FZ coincides with EZ in H2,0(∂W) under the Poincaré residue map and various identifications of cohomologies.

リンク情報
DOI
https://doi.org/10.4310/ATMP.2017.v21.n3.a1
ID情報
  • DOI : 10.4310/ATMP.2017.v21.n3.a1
  • ISSN : 1095-0753
  • ISSN : 1095-0761
  • SCOPUS ID : 85028296424

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