CICY6309

rank 2
I₂(∞) (P)
affine

Favorable Kähler-favProduct

$h^{1,1}$: 4
$h^{2,1}$: 32
$\chi$: −56
ambient factors: 4
polynomials: 6
iso-flops: 2
Coxeter rank: 2
Coxeter group: I₂(∞) (P)

Configuration matrix: 4×6 configuration
$X_{6309} = \left[\begin{array}{c|cccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 1 & 0 & 0 \\ \mathbb{P}^{3} & 1 & 0 & 2 & 0 & 1 & 0 \\ \mathbb{P}^{4} & 0 & 1 & 0 & 1 & 1 & 2 \end{array}\right]^{4,32}_{-56}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 44 & 52 \end{pmatrix}^{T}$
Coxeter diagram Gallery →
Coxeter matrix $\text{P, H} = \infty$: $\begin{pmatrix} 1 & \text{P} \\ \text{P} & 1 \end{pmatrix}$
Iso-flop reflections Kähler representation: $\hat{M}_1$ : row 3, Type 2
$\hat{M}_1 = \begin{pmatrix} 1 & 0 & 2 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 2 & 1 \end{pmatrix}$
$\hat{M}_2$ : row 4, Type 2
$\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & -1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 6309, H11 -> 4, H21 -> 32, C2 -> {24, 24, 44, 52}, Conf -> {{1, 1, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {1, 0, 2, 0, 1, 0}, {0, 1, 0, 1, 1, 2}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{3, "Type 2"}, {4, "Type 2"}}, KahlerRefGens -> {{{1, 0, 2, 0}, {0, 1, 1, 0}, {0, 0, -1, 0}, {0, 0, 2, 1}}, {{1, 0, 0, 2}, {0, 1, 0, 2}, {0, 0, 1, 2}, {0, 0, 0, -1}}}, CoxeterMat -> {{1, P}, {P, 1}}|>

Plain text

Num           : 6309
H11           : 4
H21           : 32
C2            : {24, 24, 44, 52}
Conf          : {{1, 1, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {1, 0, 2, 0, 1, 0}, {0, 1, 0, 1, 1, 2}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{3, "Type 2"}, {4, "Type 2"}}
KahlerRefGens : {{{1, 0, 2, 0}, {0, 1, 1, 0}, {0, 0, -1, 0}, {0, 0, 2, 1}}, {{1, 0, 0, 2}, {0, 1, 0, 2}, {0, 0, 1, 2}, {0, 0, 0, -1}}}
CoxeterMat    : {{1, P}, {P, 1}}