CICY Coxeter DB | 6168

CICY6168

  • rank 2
  • I₂(2)
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
5
h2,1h^{2,1}
33
χ\chi
−56
ambient factors
5
polynomials
6
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(2)
Configuration matrix
5×6 configuration
X6168=[P1110000P1001100P1001010P2001002P4110111]−565,33X_{6168} = \left[\begin{array}{c|cccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 1 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 1 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 1 & 0 & 0 & 2 \\ \mathbb{P}^{4} & 1 & 1 & 0 & 1 & 1 & 1 \end{array}\right]^{5,33}_{-56}
Second Chern class
c2(X)⋅Di=(2424243652)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 36 & 52 \end{pmatrix}^{T}
Coxeter diagram Gallery →
Coxeter matrix
(1221)\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}
Iso-flop reflections Kähler representation
M^1\hat{M}_1: row 1, Type 1a
M^1=(−1000001000001000001010001)\hat{M}_1 = \begin{pmatrix} -1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 4, Type 2
M^2=(100000102000120000−1000011)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 2 & 0 \\ 0 & 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 & 1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 6168, H11 -> 5, H21 -> 33, C2 -> {24, 24, 24, 36, 52}, Conf -> {{1, 1, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 1, 0, 0, 2}, {1, 1, 0, 1, 1, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 1a"}, {4, "Type 2"}}, KahlerRefGens -> {{{-1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {1, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 2, 0}, {0, 0, 1, 2, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>
Plain text 
Num           : 6168
H11           : 5
H21           : 33
C2            : {24, 24, 24, 36, 52}
Conf          : {{1, 1, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 1, 0, 0, 2}, {1, 1, 0, 1, 1, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 1a"}, {4, "Type 2"}}
KahlerRefGens : {{{-1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {1, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 2, 0}, {0, 0, 1, 2, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}}}
CoxeterMat    : {{1, 2}, {2, 1}}