CICY4357

rank 2
I₂(2)
finite

Favorable Kähler-favProduct

$h^{1,1}$: 8
$h^{2,1}$: 28
$\chi$: −40
ambient factors: 8
polynomials: 9
iso-flops: 2
Coxeter rank: 2
Coxeter group: I₂(2)

Configuration matrix: 8×9 configuration
$X_{4357} = \left[\begin{array}{c|ccccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 \\ \mathbb{P}^{2} & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 \\ \mathbb{P}^{2} & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 \\ \mathbb{P}^{3} & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \end{array}\right]^{8,28}_{-40}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 24 & 36 & 36 & 44 \end{pmatrix}^{T}$
Coxeter diagram Gallery →
Coxeter matrix: $\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}$
Iso-flop reflections Kähler representation: $\hat{M}_1$ : row 5, Type 2
$\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}$
$\hat{M}_2$ : row 8, Type 1b
$\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 4357, H11 -> 8, H21 -> 28, C2 -> {24, 24, 24, 24, 24, 36, 36, 44}, Conf -> {{1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 2}, {0, 0, 1, 0, 1, 0, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 1, 1, 1, 0}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{5, "Type 2"}, {8, "Type 1b"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 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, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, -1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>

Plain text

Num           : 4357
H11           : 8
H21           : 28
C2            : {24, 24, 24, 24, 24, 36, 36, 44}
Conf          : {{1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 2}, {0, 0, 1, 0, 1, 0, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 1, 1, 1, 0}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{5, "Type 2"}, {8, "Type 1b"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 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, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, -1}}}
CoxeterMat    : {{1, 2}, {2, 1}}