CICY Coxeter DB | 7688

CICY7688

  • rank 2
  • I₂(∞) (P)
  • affine
Favorable Kähler-favProduct
h1,1h^{1,1}
5
h2,1h^{2,1}
51
χ\chi
−92
ambient factors
5
polynomials
6
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(∞) (P)
Configuration matrix
5×6 configuration
X7688=[P1110000P1001100P2000021P2101001P3010120]−925,51X_{7688} = \left[\begin{array}{c|cccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 1 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 0 & 0 & 2 & 1 \\ \mathbb{P}^{2} & 1 & 0 & 1 & 0 & 0 & 1 \\ \mathbb{P}^{3} & 0 & 1 & 0 & 1 & 2 & 0 \end{array}\right]^{5,51}_{-92}
Second Chern class
c2(X)⋅Di=(2424363644)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 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 3, Type 2
M^1=(100000100000−1000021000201)\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 2 & 1 & 0 \\ 0 & 0 & 2 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 5, Type 2
M^2=(100020100200102000100000−1)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & -1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 7688, H11 -> 5, H21 -> 51, C2 -> {24, 24, 36, 36, 44}, Conf -> {{1, 1, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 2, 1}, {1, 0, 1, 0, 0, 1}, {0, 1, 0, 1, 2, 0}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{3, "Type 2"}, {5, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 2, 1, 0}, {0, 0, 2, 0, 1}}, {{1, 0, 0, 0, 2}, {0, 1, 0, 0, 2}, {0, 0, 1, 0, 2}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, -1}}}, CoxeterMat -> {{1, P}, {P, 1}}|>
Plain text 
Num           : 7688
H11           : 5
H21           : 51
C2            : {24, 24, 36, 36, 44}
Conf          : {{1, 1, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 2, 1}, {1, 0, 1, 0, 0, 1}, {0, 1, 0, 1, 2, 0}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{3, "Type 2"}, {5, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 2, 1, 0}, {0, 0, 2, 0, 1}}, {{1, 0, 0, 0, 2}, {0, 1, 0, 0, 2}, {0, 0, 1, 0, 2}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, -1}}}
CoxeterMat    : {{1, P}, {P, 1}}