CICY7784

rank 2
I₂(∞) (P)
affine

Favorable Kähler-favProduct

$h^{1,1}$: 4
$h^{2,1}$: 56
$\chi$: −104
ambient factors: 4
polynomials: 4
iso-flops: 2
Coxeter rank: 2
Coxeter group: I₂(∞) (P)

Configuration matrix: 4×4 configuration
$X_{7784} = \left[\begin{array}{c|cccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 \\ \mathbb{P}^{2} & 2 & 0 & 1 & 0 \\ \mathbb{P}^{2} & 2 & 0 & 0 & 1 \\ \mathbb{P}^{2} & 0 & 1 & 1 & 1 \end{array}\right]^{4,56}_{-104}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 24 & 36 & 36 & 36 \end{pmatrix}^{T}$
Coxeter diagram Gallery →
Coxeter matrix $\text{P, H} = \infty$: $\begin{pmatrix} 1 & \text{P} \\ \text{P} & 1 \end{pmatrix}$
Iso-flop reflections Kähler representation: $\hat{M}_1$ : row 2, Type 2
$\hat{M}_1 = \begin{pmatrix} 1 & 1 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 2 & 1 & 0 \\ 0 & 2 & 0 & 1 \end{pmatrix}$
$\hat{M}_2$ : row 3, Type 2
$\hat{M}_2 = \begin{pmatrix} 1 & 0 & 1 & 0 \\ 0 & 1 & 2 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 2 & 1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 7784, H11 -> 4, H21 -> 56, C2 -> {24, 36, 36, 36}, Conf -> {{1, 1, 0, 0}, {2, 0, 1, 0}, {2, 0, 0, 1}, {0, 1, 1, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{2, "Type 2"}, {3, "Type 2"}}, KahlerRefGens -> {{{1, 1, 0, 0}, {0, -1, 0, 0}, {0, 2, 1, 0}, {0, 2, 0, 1}}, {{1, 0, 1, 0}, {0, 1, 2, 0}, {0, 0, -1, 0}, {0, 0, 2, 1}}}, CoxeterMat -> {{1, P}, {P, 1}}|>

Plain text

Num           : 7784
H11           : 4
H21           : 56
C2            : {24, 36, 36, 36}
Conf          : {{1, 1, 0, 0}, {2, 0, 1, 0}, {2, 0, 0, 1}, {0, 1, 1, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{2, "Type 2"}, {3, "Type 2"}}
KahlerRefGens : {{{1, 1, 0, 0}, {0, -1, 0, 0}, {0, 2, 1, 0}, {0, 2, 0, 1}}, {{1, 0, 1, 0}, {0, 1, 2, 0}, {0, 0, -1, 0}, {0, 0, 2, 1}}}
CoxeterMat    : {{1, P}, {P, 1}}