CICY6915

rank 2
I₂(2)
finite

Favorable Kähler-favProduct

$h^{1,1}$: 5
$h^{2,1}$: 37
$\chi$: −64
ambient factors: 5
polynomials: 3
iso-flops: 2
Coxeter rank: 2
Coxeter group: I₂(2)

Configuration matrix: 5×3 configuration
$X_{6915} = \left[\begin{array}{c|ccc} \mathbb{P}^{1} & 1 & 1 & 0 \\ \mathbb{P}^{1} & 1 & 0 & 1 \\ \mathbb{P}^{1} & 0 & 0 & 2 \\ \mathbb{P}^{1} & 2 & 0 & 0 \\ \mathbb{P}^{2} & 1 & 1 & 1 \end{array}\right]^{5,37}_{-64}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 36 \end{pmatrix}^{T}$
Coxeter diagram Gallery →
Coxeter matrix: $\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}$
Iso-flop reflections Kähler representation: $\hat{M}_1$ : row 3, Type 2
$\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 \end{pmatrix}$
$\hat{M}_2$ : row 4, Type 2
$\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 & 1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 6915, H11 -> 5, H21 -> 37, C2 -> {24, 24, 24, 24, 36}, Conf -> {{1, 1, 0}, {1, 0, 1}, {0, 0, 2}, {2, 0, 0}, {1, 1, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{3, "Type 2"}, {4, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0}, {0, 1, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 1, 0, 1}}, {{1, 0, 0, 1, 0}, {0, 1, 0, 1, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>

Plain text

Num           : 6915
H11           : 5
H21           : 37
C2            : {24, 24, 24, 24, 36}
Conf          : {{1, 1, 0}, {1, 0, 1}, {0, 0, 2}, {2, 0, 0}, {1, 1, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{3, "Type 2"}, {4, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0, 0}, {0, 1, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 1, 0, 1}}, {{1, 0, 0, 1, 0}, {0, 1, 0, 1, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}}}
CoxeterMat    : {{1, 2}, {2, 1}}