CICY6220

rank 2
I₂(2)
finite

Favorable Kähler-favProduct

$h^{1,1}$: 3
$h^{2,1}$: 31
$\chi$: −56
ambient factors: 3
polynomials: 4
iso-flops: 2
Coxeter rank: 2
Coxeter group: I₂(2)

Configuration matrix: 3×4 configuration
$X_{6220} = \left[\begin{array}{c|cccc} \mathbb{P}^{2} & 2 & 1 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 2 & 1 \\ \mathbb{P}^{3} & 1 & 1 & 1 & 1 \end{array}\right]^{3,31}_{-56}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 36 & 36 & 40 \end{pmatrix}^{T}$
Coxeter diagram Gallery →
Coxeter matrix: $\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}$
Iso-flop reflections Kähler representation: $\hat{M}_1$ : row 1, Type 2
$\hat{M}_1 = \begin{pmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 3 & 0 & 1 \end{pmatrix}$
$\hat{M}_2$ : row 2, Type 2
$\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 3 & 1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 6220, H11 -> 3, H21 -> 31, C2 -> {36, 36, 40}, Conf -> {{2, 1, 0, 0}, {0, 0, 2, 1}, {1, 1, 1, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 2"}, {2, "Type 2"}}, KahlerRefGens -> {{{-1, 0, 0}, {0, 1, 0}, {3, 0, 1}}, {{1, 0, 0}, {0, -1, 0}, {0, 3, 1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>

Plain text

Num           : 6220
H11           : 3
H21           : 31
C2            : {36, 36, 40}
Conf          : {{2, 1, 0, 0}, {0, 0, 2, 1}, {1, 1, 1, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 2"}, {2, "Type 2"}}
KahlerRefGens : {{{-1, 0, 0}, {0, 1, 0}, {3, 0, 1}}, {{1, 0, 0}, {0, -1, 0}, {0, 3, 1}}}
CoxeterMat    : {{1, 2}, {2, 1}}