CICY1357

rank 1
ℤ₂
finite

Favorable Kähler-favProduct

$h^{1,1}$: 9
$h^{2,1}$: 21
$\chi$: −24
ambient factors: 9
polynomials: 11
iso-flops: 1
Coxeter rank: 1
Coxeter group: ℤ₂

Configuration matrix: 9×11 configuration
$X_{1357} = \left[\begin{array}{c|ccccccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 1 & 0 \\ \mathbb{P}^{2} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\ \mathbb{P}^{2} & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{array}\right]^{9,21}_{-24}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 36 & 36 & 36 & 36 & 36 \end{pmatrix}^{T}$
Coxeter diagram Gallery →
Coxeter matrix: $\begin{pmatrix} 1 \end{pmatrix}$
Iso-flop reflections Kähler representation: $\hat{M}_1$ : row 5, Type 2
$\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 2 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 1357, H11 -> 9, H21 -> 21, C2 -> {24, 24, 24, 24, 36, 36, 36, 36, 36}, Conf -> {{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{5, "Type 2"}}, KahlerRefGens -> {{{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, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 0, 0, 2, 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           : 1357
H11           : 9
H21           : 21
C2            : {24, 24, 24, 24, 36, 36, 36, 36, 36}
Conf          : {{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{5, "Type 2"}}
KahlerRefGens : {{{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, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 0, 0, 2, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1}}}
CoxeterMat    : {{1}}