CICY Coxeter DB | 7758

CICY7758

  • rank 1
  • ℤ₂
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
2
h2,1h^{2,1}
52
χ\chi
−100
ambient factors
2
polynomials
3
iso-flops
1
Coxeter rank
1
Coxeter group
ℤ₂
Configuration matrix
2×3 configuration
X7758=[P2021P4212]−1002,52X_{7758} = \left[\begin{array}{c|ccc} \mathbb{P}^{2} & 0 & 2 & 1 \\ \mathbb{P}^{4} & 2 & 1 & 2 \end{array}\right]^{2,52}_{-100}
Second Chern class
c2(X)⋅Di=(3652)Tc_2(X)\cdot D_i = \begin{pmatrix} 36 & 52 \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=(−1051)\hat{M}_1 = \begin{pmatrix} -1 & 0 \\ 5 & 1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 7758, H11 -> 2, H21 -> 52, C2 -> {36, 52}, Conf -> {{0, 2, 1}, {2, 1, 2}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 2"}}, KahlerRefGens -> {{{-1, 0}, {5, 1}}}, CoxeterMat -> {{1}}|>
Plain text 
Num           : 7758
H11           : 2
H21           : 52
C2            : {36, 52}
Conf          : {{0, 2, 1}, {2, 1, 2}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 2"}}
KahlerRefGens : {{{-1, 0}, {5, 1}}}
CoxeterMat    : {{1}}