CICY Coxeter DB | 7054

CICY7054

  • rank 2
  • I₂(∞) (P)
  • affine
Favorable Kähler-favProduct
h1,1h^{1,1}
4
h2,1h^{2,1}
38
χ\chi
−68
ambient factors
4
polynomials
5
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(∞) (P)
Configuration matrix
4×5 configuration
X7054=[P111000P200210P210011P301102]−684,38X_{7054} = \left[\begin{array}{c|ccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 2 & 1 & 0 \\ \mathbb{P}^{2} & 1 & 0 & 0 & 1 & 1 \\ \mathbb{P}^{3} & 0 & 1 & 1 & 0 & 2 \end{array}\right]^{4,38}_{-68}
Second Chern class
c2(X)⋅Di=(24363644)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 36 & 36 & 44 \end{pmatrix}^{T}
Coxeter diagram Gallery →
P
Coxeter matrixP, H=∞\text{P, H} = \infty
(1PP1)\begin{pmatrix} 1 & \text{P} \\ \text{P} & 1 \end{pmatrix}
Iso-flop reflections Kähler representation
M^1\hat{M}_1: row 2, Type 2
M^1=(10000−10002100101)\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 2 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 4, Type 2
M^2=(100201040011000−1)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 4 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & -1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 7054, H11 -> 4, H21 -> 38, C2 -> {24, 36, 36, 44}, Conf -> {{1, 1, 0, 0, 0}, {0, 0, 2, 1, 0}, {1, 0, 0, 1, 1}, {0, 1, 1, 0, 2}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{2, "Type 2"}, {4, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 2, 1, 0}, {0, 1, 0, 1}}, {{1, 0, 0, 2}, {0, 1, 0, 4}, {0, 0, 1, 1}, {0, 0, 0, -1}}}, CoxeterMat -> {{1, P}, {P, 1}}|>
Plain text 
Num           : 7054
H11           : 4
H21           : 38
C2            : {24, 36, 36, 44}
Conf          : {{1, 1, 0, 0, 0}, {0, 0, 2, 1, 0}, {1, 0, 0, 1, 1}, {0, 1, 1, 0, 2}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{2, "Type 2"}, {4, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 2, 1, 0}, {0, 1, 0, 1}}, {{1, 0, 0, 2}, {0, 1, 0, 4}, {0, 0, 1, 1}, {0, 0, 0, -1}}}
CoxeterMat    : {{1, P}, {P, 1}}