Geometry and arithmetic of certain double octic Calabi-Yau manifolds

被引：11
|
作者：
Cynk, S
Meyer, C
机构：
[1] Jagiellonian Univ, Inst Matemat, PL-30059 Krakow, Poland
[2] Univ Mainz, Fachbereich Math & Informat, D-55099 Mainz, Germany
来源：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2005年 / 48卷 / 02期
关键词：
Calabi-Yau; double coverings; modular forms;
D O I：
10.4153/CMB-2005-016-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study Calabi-Yau manifolds constructed as double coverings of P-3 branched along an octic surface. We give a list of 87 examples corresponding to arrangements of eight planes defined over Q. The Hodge numbers are computed for all examples. There are 10 rigid Calabi-Yau manifolds and 14 families with h(1,2) = 1. The modularity conjecture is verified for all the rigid examples.
引用
收藏
页码：180 / 194
页数：15
相关论文
共 50 条
  • [1] MODULARITY OF SOME NONRIGID DOUBLE OCTIC CALABI-YAU THREEFOLDS
    Cynk, Slawomir
    Meyer, Christian
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2008, 38 (06) : 1937 - 1958
  • [2] Periods of rigid double octic Calabi-Yau threefolds
    Cynk, Slawomir
    van Straten, Duco
    ANNALES POLONICI MATHEMATICI, 2019, 123 (01) : 243 - 258
  • [3] Periods of singular double octic Calabi-Yau threefolds and modular forms
    Chmiel, Tymoteusz
    Cynk, Slawomir
    MATHEMATISCHE NACHRICHTEN, 2023, 296 (08) : 3257 - 3271
  • [4] Modularity of a certain Calabi-Yau threefold
    Ahlgren, S
    Ono, K
    MONATSHEFTE FUR MATHEMATIK, 2000, 129 (03): : 177 - 190
  • [5] Symplectic Calabi-Yau 6-manifolds
    Akhmedov, Anar
    ADVANCES IN MATHEMATICS, 2014, 262 : 115 - 125
  • [6] Computing period integrals of rigid double octic Calabi-Yau threefolds with Picard-Fuchs operator
    Chmiel, Tymoteusz
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2021, 225 (05)
  • [7] Modularity of a certain Calabi-Yau threefold and combinatorial congruences
    Mortenson, E
    RAMANUJAN JOURNAL, 2006, 11 (01) : 5 - 39
  • [8] Modularity of a certain Calabi-Yau threefold and combinatorial congruences
    Eric Mortenson
    The Ramanujan Journal, 2006, 11 : 5 - 39
  • [9] Enumerative meaning of mirror maps for toric Calabi-Yau manifolds
    Chan, Kwokwai
    Lau, Siu-Cheong
    Tseng, Hsian-Hua
    ADVANCES IN MATHEMATICS, 2013, 244 : 605 - 625
  • [10] One-dimensional super Calabi-Yau manifolds and their mirrors
    Noja, S.
    Cacciatori, S. L.
    Piazza, F. Dalla
    Marrani, A.
    Re, R.
    JOURNAL OF HIGH ENERGY PHYSICS, 2017, (04):
12345