CICY Coxeter DB | 2822

CICY2822

  • rank 2
  • I₂(2)
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
7
h2,1h^{2,1}
23
χ\chi
−32
ambient factors
7
polynomials
7
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(2)
Configuration matrix
7×7 configuration
X2822=[P11100000P10011000P10010100P10000011P10000020P21010010P30101101]−327,23X_{2822} = \left[\begin{array}{c|ccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 0 & 2 & 0 \\ \mathbb{P}^{2} & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ \mathbb{P}^{3} & 0 & 1 & 0 & 1 & 1 & 0 & 1 \end{array}\right]^{7,23}_{-32}
Second Chern class
c2(X)⋅Di=(24242424243644)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 24 & 36 & 44 \end{pmatrix}^{T}
Coxeter diagram Gallery →
Coxeter matrix
(1221)\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}
Iso-flop reflections Kähler representation
M^1\hat{M}_1: row 5, Type 2
M^1=(10000000100000001000000011000000−10000001100000001)\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 7, Type 1b
M^2=(100000101000010010001000100100001000000010000000−1)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & -1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 2822, H11 -> 7, H21 -> 23, C2 -> {24, 24, 24, 24, 24, 36, 44}, Conf -> {{1, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, 2, 0}, {1, 0, 1, 0, 0, 1, 0}, {0, 1, 0, 1, 1, 0, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{5, "Type 2"}, {7, "Type 1b"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, -1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>
Plain text 
Num           : 2822
H11           : 7
H21           : 23
C2            : {24, 24, 24, 24, 24, 36, 44}
Conf          : {{1, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, 2, 0}, {1, 0, 1, 0, 0, 1, 0}, {0, 1, 0, 1, 1, 0, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{5, "Type 2"}, {7, "Type 1b"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, -1}}}
CoxeterMat    : {{1, 2}, {2, 1}}