CICY6723

rank 1
ℤ₂
finite

Favorable Kähler-favProduct

$h^{1,1}$: 6
$h^{2,1}$: 38
$\chi$: −64
ambient factors: 6
polynomials: 6
iso-flops: 1
Coxeter rank: 1
Coxeter group: ℤ₂

Configuration matrix: 6×6 configuration
$X_{6723} = \left[\begin{array}{c|cccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 1 & 0 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 1 & 0 & 0 & 1 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 0 & 2 \\ \mathbb{P}^{2} & 0 & 1 & 1 & 0 & 1 & 0 \\ \mathbb{P}^{3} & 1 & 0 & 0 & 1 & 1 & 1 \end{array}\right]^{6,38}_{-64}$
Second Chern class: $c_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 36 & 52 \end{pmatrix}^{T}$
Coxeter diagram Gallery →
Coxeter matrix: $\begin{pmatrix} 1 \end{pmatrix}$
Iso-flop reflections Kähler representation: $\hat{M}_1$ : row 4, Type 2
$\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 \end{pmatrix}$

Database record

Mathematica

<|Num -> 6723, H11 -> 6, H21 -> 38, C2 -> {24, 24, 24, 24, 36, 52}, Conf -> {{1, 1, 0, 0, 0, 0}, {1, 0, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 2}, {0, 1, 1, 0, 1, 0}, {1, 0, 0, 1, 1, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{4, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 1}}}, CoxeterMat -> {{1}}|>

Plain text

Num           : 6723
H11           : 6
H21           : 38
C2            : {24, 24, 24, 24, 36, 52}
Conf          : {{1, 1, 0, 0, 0, 0}, {1, 0, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 2}, {0, 1, 1, 0, 1, 0}, {1, 0, 0, 1, 1, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{4, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 1}}}
CoxeterMat    : {{1}}