CICY1375

rank 1
ℤ₂
finite

Favorable Kähler-favProduct

$h^{1,1}$: 9
$h^{2,1}$: 21
$\chi$: −24
ambient factors: 9
polynomials: 12
iso-flops: 1
Coxeter rank: 1
Coxeter group: ℤ₂

Configuration matrix: 9×12 configuration
$X_{1375} = \left[\begin{array}{c|cccccccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\ \mathbb{P}^{2} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ \mathbb{P}^{2} & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ \mathbb{P}^{3} & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \end{array}\right]^{9,21}_{-24}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 36 & 36 & 36 & 36 & 44 \end{pmatrix}^{T}$
Coxeter diagram Gallery →
Coxeter matrix: $\begin{pmatrix} 1 \end{pmatrix}$
Iso-flop reflections Kähler representation: $\hat{M}_1$ : row 9, Type 1b
$\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 1375, H11 -> 9, H21 -> 21, C2 -> {24, 24, 24, 24, 36, 36, 36, 36, 44}, Conf -> {{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1}, {1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{9, "Type 1b"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -1}}}, CoxeterMat -> {{1}}|>

Plain text

Num           : 1375
H11           : 9
H21           : 21
C2            : {24, 24, 24, 24, 36, 36, 36, 36, 44}
Conf          : {{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1}, {1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{9, "Type 1b"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -1}}}
CoxeterMat    : {{1}}