CICY Coxeter DB | 6943

CICY6943

  • rank 2
  • I₂(2)
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
6
h2,1h^{2,1}
38
χ\chi
−64
ambient factors
6
polynomials
7
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(2)
Configuration matrix
6×7 configuration
X6943=[P11100000P10011000P10000110P10000101P31010011P30101200]−646,38X_{6943} = \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 & 0 & 0 & 1 & 1 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ \mathbb{P}^{3} & 1 & 0 & 1 & 0 & 0 & 1 & 1 \\ \mathbb{P}^{3} & 0 & 1 & 0 & 1 & 2 & 0 & 0 \end{array}\right]^{6,38}_{-64}
Second Chern class
c2(X)⋅Di=(242424244444)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 44 & 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 1b
M^1=(1000100100100010100001100000−10000001)\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 6, Type 2
M^2=(10000201000200100100010100001000000−1)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 & 0 & 2 \\ 0 & 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 6943, H11 -> 6, H21 -> 38, C2 -> {24, 24, 24, 24, 44, 44}, Conf -> {{1, 1, 0, 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}, {1, 0, 1, 0, 0, 1, 1}, {0, 1, 0, 1, 2, 0, 0}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{5, "Type 1b"}, {6, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0, 2}, {0, 1, 0, 0, 0, 2}, {0, 0, 1, 0, 0, 1}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, -1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>
Plain text 
Num           : 6943
H11           : 6
H21           : 38
C2            : {24, 24, 24, 24, 44, 44}
Conf          : {{1, 1, 0, 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}, {1, 0, 1, 0, 0, 1, 1}, {0, 1, 0, 1, 2, 0, 0}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{5, "Type 1b"}, {6, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0, 2}, {0, 1, 0, 0, 0, 2}, {0, 0, 1, 0, 0, 1}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, -1}}}
CoxeterMat    : {{1, 2}, {2, 1}}