CICY Coxeter DB | 4314

CICY4314

  • rank 2
  • I₂(2)
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
7
h2,1h^{2,1}
27
χ\chi
−40
ambient factors
7
polynomials
9
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(2)
Configuration matrix
7×9 configuration
X4314=[P1110000000P1001100000P1000011000P1000000110P1001000001P3000110101P4111001010]−407,27X_{4314} = \left[\begin{array}{c|ccccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\ \mathbb{P}^{3} & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 \\ \mathbb{P}^{4} & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \end{array}\right]^{7,27}_{-40}
Second Chern class
c2(X)⋅Di=(24242424244452)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 24 & 44 & 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=(−1000000010000000100000001000000010000000101000001)\hat{M}_1 = \begin{pmatrix} -1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 6, Type 1b
M^2=(1000000010001000100100001010000011000000−100000001)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 4314, H11 -> 7, H21 -> 27, C2 -> {24, 24, 24, 24, 24, 44, 52}, Conf -> {{1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 1, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 1, 0, 1, 0, 1}, {1, 1, 1, 0, 0, 1, 0, 1, 0}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 1a"}, {6, "Type 1b"}}, KahlerRefGens -> {{{-1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {1, 0, 0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 1, 0}, {0, 0, 1, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 1, 0}, {0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 0, 1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>
Plain text 
Num           : 4314
H11           : 7
H21           : 27
C2            : {24, 24, 24, 24, 24, 44, 52}
Conf          : {{1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 1, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 1, 0, 1, 0, 1}, {1, 1, 1, 0, 0, 1, 0, 1, 0}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 1a"}, {6, "Type 1b"}}
KahlerRefGens : {{{-1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {1, 0, 0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 1, 0}, {0, 0, 1, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 1, 0}, {0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 0, 1}}}
CoxeterMat    : {{1, 2}, {2, 1}}