CICY Coxeter DB | 4042

CICY4042

  • rank 1
  • ℤ₂
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
6
h2,1h^{2,1}
26
χ\chi
−40
ambient factors
6
polynomials
8
iso-flops
1
Coxeter rank
1
Coxeter group
ℤ₂
Configuration matrix
6×8 configuration
X4042=[P111000000P100101000P100010100P211000010P210110000P400001112]−406,26X_{4042} = \left[\begin{array}{c|cccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ \mathbb{P}^{2} & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 \\ \mathbb{P}^{2} & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{4} & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 2 \end{array}\right]^{6,26}_{-40}
Second Chern class
c2(X)⋅Di=(242424363652)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 36 & 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 6, Type 2
M^1=(10000001000200100200010200001000000−1)\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 2 \\ 0 & 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 4042, H11 -> 6, H21 -> 26, C2 -> {24, 24, 24, 36, 36, 52}, Conf -> {{1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 1, 0, 0}, {1, 1, 0, 0, 0, 0, 1, 0}, {1, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 1, 2}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{6, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 2}, {0, 0, 1, 0, 0, 2}, {0, 0, 0, 1, 0, 2}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, -1}}}, CoxeterMat -> {{1}}|>
Plain text 
Num           : 4042
H11           : 6
H21           : 26
C2            : {24, 24, 24, 36, 36, 52}
Conf          : {{1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 1, 0, 0}, {1, 1, 0, 0, 0, 0, 1, 0}, {1, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 1, 2}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{6, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 2}, {0, 0, 1, 0, 0, 2}, {0, 0, 0, 1, 0, 2}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, -1}}}
CoxeterMat    : {{1}}