CICY Coxeter DB | 7822

CICY7822

  • rank 1
  • ℤ₂
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
2
h2,1h^{2,1}
58
χ\chi
−112
ambient factors
2
polynomials
3
iso-flops
1
Coxeter rank
1
Coxeter group
ℤ₂
Configuration matrix
2×3 configuration
X7822=[P1002P5222]−1122,58X_{7822} = \left[\begin{array}{c|ccc} \mathbb{P}^{1} & 0 & 0 & 2 \\ \mathbb{P}^{5} & 2 & 2 & 2 \end{array}\right]^{2,58}_{-112}
Second Chern class
c2(X)⋅Di=(2456)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 56 \end{pmatrix}^{T}
Coxeter diagram Gallery →
Coxeter matrix
(1)\begin{pmatrix} 1 \end{pmatrix}
Iso-flop reflections Kähler representation
M^1\hat{M}_1: row 1, Type 2
M^1=(−1021)\hat{M}_1 = \begin{pmatrix} -1 & 0 \\ 2 & 1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 7822, H11 -> 2, H21 -> 58, C2 -> {24, 56}, Conf -> {{0, 0, 2}, {2, 2, 2}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 2"}}, KahlerRefGens -> {{{-1, 0}, {2, 1}}}, CoxeterMat -> {{1}}|>
Plain text 
Num           : 7822
H11           : 2
H21           : 58
C2            : {24, 56}
Conf          : {{0, 0, 2}, {2, 2, 2}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 2"}}
KahlerRefGens : {{{-1, 0}, {2, 1}}}
CoxeterMat    : {{1}}