CICY7880

rank 2
I₂(∞) (P)
affine

Favorable Kähler-favProduct

$h^{1,1}$: 3
$h^{2,1}$: 75
$\chi$: −144
ambient factors: 3
polynomials: 1
iso-flops: 2
Coxeter rank: 2
Coxeter group: I₂(∞) (P)

Configuration matrix: 3×1 configuration
$X_{7880} = \left[\begin{array}{c|c} \mathbb{P}^{1} & 2 \\ \mathbb{P}^{1} & 2 \\ \mathbb{P}^{2} & 3 \end{array}\right]^{3,75}_{-144}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 36 \end{pmatrix}^{T}$
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 1, Type 2
$\hat{M}_1 = \begin{pmatrix} -1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 0 & 1 \end{pmatrix}$
$\hat{M}_2$ : row 2, Type 2
$\hat{M}_2 = \begin{pmatrix} 1 & 2 & 0 \\ 0 & -1 & 0 \\ 0 & 3 & 1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 7880, H11 -> 3, H21 -> 75, C2 -> {24, 24, 36}, Conf -> {{2}, {2}, {3}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 2"}, {2, "Type 2"}}, KahlerRefGens -> {{{-1, 0, 0}, {2, 1, 0}, {3, 0, 1}}, {{1, 2, 0}, {0, -1, 0}, {0, 3, 1}}}, CoxeterMat -> {{1, P}, {P, 1}}|>

Plain text

Num           : 7880
H11           : 3
H21           : 75
C2            : {24, 24, 36}
Conf          : {{2}, {2}, {3}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 2"}, {2, "Type 2"}}
KahlerRefGens : {{{-1, 0, 0}, {2, 1, 0}, {3, 0, 1}}, {{1, 2, 0}, {0, -1, 0}, {0, 3, 1}}}
CoxeterMat    : {{1, P}, {P, 1}}