CICY Coxeter DB | 5704

CICY5704

  • rank 1
  • ℤ₂
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
6
h2,1h^{2,1}
32
χ\chi
−52
ambient factors
6
polynomials
9
iso-flops
1
Coxeter rank
1
Coxeter group
ℤ₂
Configuration matrix
6×9 configuration
X5704=[P1110000000P1001010000P1000101000P2100100100P2001000110P5010011012]−526,32X_{5704} = \left[\begin{array}{c|ccccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{2} & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 0 \\ \mathbb{P}^{5} & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 2 \end{array}\right]^{6,32}_{-52}
Second Chern class
c2(X)⋅Di=(242424363656)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 36 & 36 & 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 6, Type 2
M^1=(10000201000200100200010000001200000−1)\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 & 0 & 2 \\ 0 & 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & -1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 5704, H11 -> 6, H21 -> 32, C2 -> {24, 24, 24, 36, 36, 56}, Conf -> {{1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 0, 1, 1, 0}, {0, 1, 0, 0, 1, 1, 0, 1, 2}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{6, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 2}, {0, 1, 0, 0, 0, 2}, {0, 0, 1, 0, 0, 2}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 2}, {0, 0, 0, 0, 0, -1}}}, CoxeterMat -> {{1}}|>
Plain text 
Num           : 5704
H11           : 6
H21           : 32
C2            : {24, 24, 24, 36, 36, 56}
Conf          : {{1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 0, 1, 1, 0}, {0, 1, 0, 0, 1, 1, 0, 1, 2}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{6, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 2}, {0, 1, 0, 0, 0, 2}, {0, 0, 1, 0, 0, 2}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 2}, {0, 0, 0, 0, 0, -1}}}
CoxeterMat    : {{1}}