CICY7721

rank 2
I₂(2)
finite

Favorable Kähler-favProduct

$h^{1,1}$: 3
$h^{2,1}$: 51
$\chi$: −96
ambient factors: 3
polynomials: 5
iso-flops: 2
Coxeter rank: 2
Coxeter group: I₂(2)

Configuration matrix: 3×5 configuration
$X_{7721} = \left[\begin{array}{c|ccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{3} & 0 & 0 & 2 & 1 & 1 \\ \mathbb{P}^{4} & 1 & 1 & 1 & 1 & 1 \end{array}\right]^{3,51}_{-96}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 24 & 44 & 52 \end{pmatrix}^{T}$
Coxeter diagram Gallery →
Coxeter matrix: $\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}$
Iso-flop reflections Kähler representation: $\hat{M}_1$ : row 1, Type 1a
$\hat{M}_1 = \begin{pmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{pmatrix}$
$\hat{M}_2$ : row 2, Type 2
$\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 5 & 1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 7721, H11 -> 3, H21 -> 51, C2 -> {24, 44, 52}, Conf -> {{1, 1, 0, 0, 0}, {0, 0, 2, 1, 1}, {1, 1, 1, 1, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 1a"}, {2, "Type 2"}}, KahlerRefGens -> {{{-1, 0, 0}, {0, 1, 0}, {1, 0, 1}}, {{1, 0, 0}, {0, -1, 0}, {0, 5, 1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>

Plain text

Num           : 7721
H11           : 3
H21           : 51
C2            : {24, 44, 52}
Conf          : {{1, 1, 0, 0, 0}, {0, 0, 2, 1, 1}, {1, 1, 1, 1, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 1a"}, {2, "Type 2"}}
KahlerRefGens : {{{-1, 0, 0}, {0, 1, 0}, {1, 0, 1}}, {{1, 0, 0}, {0, -1, 0}, {0, 5, 1}}}
CoxeterMat    : {{1, 2}, {2, 1}}