CICY4321

rank 1
ℤ₂
finite

Favorable Kähler-favProduct

$h^{1,1}$: 7
$h^{2,1}$: 27
$\chi$: −40
ambient factors: 7
polynomials: 9
iso-flops: 1
Coxeter rank: 1
Coxeter group: ℤ₂

Configuration matrix: 7×9 configuration
$X_{4321} = \left[\begin{array}{c|ccccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ \mathbb{P}^{3} & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 \\ \mathbb{P}^{4} & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \end{array}\right]^{7,27}_{-40}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 24 & 44 & 50 \end{pmatrix}^{T}$
Coxeter diagram Gallery →
Coxeter matrix: $\begin{pmatrix} 1 \end{pmatrix}$
Iso-flop reflections Kähler representation: $\hat{M}_1$ : row 6, Type 1b
$\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 4321, H11 -> 7, H21 -> 27, C2 -> {24, 24, 24, 24, 24, 44, 50}, Conf -> {{1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 1, 1, 1, 0}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{6, "Type 1b"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 1, 0}, {0, 0, 1, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 0, 1}}}, CoxeterMat -> {{1}}|>

Plain text

Num           : 4321
H11           : 7
H21           : 27
C2            : {24, 24, 24, 24, 24, 44, 50}
Conf          : {{1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 1, 1, 1, 0}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{6, "Type 1b"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 1, 0}, {0, 0, 1, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 0, 1}}}
CoxeterMat    : {{1}}