CICY Coxeter DB | 6543

CICY6543

  • rank 2
  • I₂(2)
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
5
h2,1h^{2,1}
35
χ\chi
−60
ambient factors
5
polynomials
6
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(2)
Configuration matrix
5×6 configuration
X6543=[P1110000P1000002P2001020P2101100P3010111]−605,35X_{6543} = \left[\begin{array}{c|cccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 0 & 2 \\ \mathbb{P}^{2} & 0 & 0 & 1 & 0 & 2 & 0 \\ \mathbb{P}^{2} & 1 & 0 & 1 & 1 & 0 & 0 \\ \mathbb{P}^{3} & 0 & 1 & 0 & 1 & 1 & 1 \end{array}\right]^{5,35}_{-60}
Second Chern class
c2(X)⋅Di=(2424363652)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 36 & 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 2, Type 2
M^1=(100000−1000001000001001001)\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 \\ 0 & 1 & 0 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 3, Type 2
M^2=(100000100000−1000021000101)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 2 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 6543, H11 -> 5, H21 -> 35, C2 -> {24, 24, 36, 36, 52}, Conf -> {{1, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 2}, {0, 0, 1, 0, 2, 0}, {1, 0, 1, 1, 0, 0}, {0, 1, 0, 1, 1, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{2, "Type 2"}, {3, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 1, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 2, 1, 0}, {0, 0, 1, 0, 1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>
Plain text 
Num           : 6543
H11           : 5
H21           : 35
C2            : {24, 24, 36, 36, 52}
Conf          : {{1, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 2}, {0, 0, 1, 0, 2, 0}, {1, 0, 1, 1, 0, 0}, {0, 1, 0, 1, 1, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{2, "Type 2"}, {3, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 1, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 2, 1, 0}, {0, 0, 1, 0, 1}}}
CoxeterMat    : {{1, 2}, {2, 1}}