CICY Coxeter DB | 5112

CICY5112

  • rank 2
  • I₂(2)
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
6
h2,1h^{2,1}
30
χ\chi
−48
ambient factors
6
polynomials
4
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(2)
Configuration matrix
6×4 configuration
X5112=[P11100P11010P11001P10002P12000P20111]−486,30X_{5112} = \left[\begin{array}{c|cccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 \\ \mathbb{P}^{1} & 1 & 0 & 1 & 0 \\ \mathbb{P}^{1} & 1 & 0 & 0 & 1 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 2 \\ \mathbb{P}^{1} & 2 & 0 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 1 & 1 & 1 \end{array}\right]^{6,30}_{-48}
Second Chern class
c2(X)⋅Di=(242424242436)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 24 & 36 \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 4, Type 2
M^1=(100000010000001100000−100000010000101)\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 5, Type 2
M^2=(1000100100100010100001000000−10000001)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 5112, H11 -> 6, H21 -> 30, C2 -> {24, 24, 24, 24, 24, 36}, Conf -> {{1, 1, 0, 0}, {1, 0, 1, 0}, {1, 0, 0, 1}, {0, 0, 0, 2}, {2, 0, 0, 0}, {0, 1, 1, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{4, "Type 2"}, {5, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 1}}, {{1, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>
Plain text 
Num           : 5112
H11           : 6
H21           : 30
C2            : {24, 24, 24, 24, 24, 36}
Conf          : {{1, 1, 0, 0}, {1, 0, 1, 0}, {1, 0, 0, 1}, {0, 0, 0, 2}, {2, 0, 0, 0}, {0, 1, 1, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{4, "Type 2"}, {5, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 1}}, {{1, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}}}
CoxeterMat    : {{1, 2}, {2, 1}}