CICY Coxeter DB | 3134

CICY3134

  • rank 1
  • ℤ₂
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
7
h2,1h^{2,1}
25
χ\chi
−36
ambient factors
7
polynomials
9
iso-flops
1
Coxeter rank
1
Coxeter group
ℤ₂
Configuration matrix
7×9 configuration
X3134=[P1110000000P1001100000P1000011000P1100000100P2001000011P3100010011P3010101100]−367,25X_{3134} = \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} & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 \\ \mathbb{P}^{3} & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 \\ \mathbb{P}^{3} & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 \end{array}\right]^{7,25}_{-36}
Second Chern class
c2(X)⋅Di=(24242424364444)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 36 & 44 & 44 \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 7, Type 1b
M^1=(100000101000010010001000100100001000000010000000−1)\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & -1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 3134, H11 -> 7, H21 -> 25, C2 -> {24, 24, 24, 24, 36, 44, 44}, 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}, {1, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 1, 1}, {1, 0, 0, 0, 1, 0, 0, 1, 1}, {0, 1, 0, 1, 0, 1, 1, 0, 0}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{7, "Type 1b"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, -1}}}, CoxeterMat -> {{1}}|>
Plain text 
Num           : 3134
H11           : 7
H21           : 25
C2            : {24, 24, 24, 24, 36, 44, 44}
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}, {1, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 1, 1}, {1, 0, 0, 0, 1, 0, 0, 1, 1}, {0, 1, 0, 1, 0, 1, 1, 0, 0}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{7, "Type 1b"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, -1}}}
CoxeterMat    : {{1}}