CICY Coxeter DB | 6778

CICY6778

  • rank 2
  • I₂(2)
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
4
h2,1h^{2,1}
36
χ\chi
−64
ambient factors
4
polynomials
4
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(2)
Configuration matrix
4×4 configuration
X6778=[P11100P12000P21011P30121]−644,36X_{6778} = \left[\begin{array}{c|cccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 \\ \mathbb{P}^{1} & 2 & 0 & 0 & 0 \\ \mathbb{P}^{2} & 1 & 0 & 1 & 1 \\ \mathbb{P}^{3} & 0 & 1 & 2 & 1 \end{array}\right]^{4,36}_{-64}
Second Chern class
c2(X)⋅Di=(24243644)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 36 & 44 \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=(11000−10001100001)\hat{M}_1 = \begin{pmatrix} 1 & 1 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 4, Type 2
M^2=(100201000013000−1)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & -1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 6778, H11 -> 4, H21 -> 36, C2 -> {24, 24, 36, 44}, Conf -> {{1, 1, 0, 0}, {2, 0, 0, 0}, {1, 0, 1, 1}, {0, 1, 2, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{2, "Type 2"}, {4, "Type 2"}}, KahlerRefGens -> {{{1, 1, 0, 0}, {0, -1, 0, 0}, {0, 1, 1, 0}, {0, 0, 0, 1}}, {{1, 0, 0, 2}, {0, 1, 0, 0}, {0, 0, 1, 3}, {0, 0, 0, -1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>
Plain text 
Num           : 6778
H11           : 4
H21           : 36
C2            : {24, 24, 36, 44}
Conf          : {{1, 1, 0, 0}, {2, 0, 0, 0}, {1, 0, 1, 1}, {0, 1, 2, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{2, "Type 2"}, {4, "Type 2"}}
KahlerRefGens : {{{1, 1, 0, 0}, {0, -1, 0, 0}, {0, 1, 1, 0}, {0, 0, 0, 1}}, {{1, 0, 0, 2}, {0, 1, 0, 0}, {0, 0, 1, 3}, {0, 0, 0, -1}}}
CoxeterMat    : {{1, 2}, {2, 1}}