CICY Coxeter DB | 3400

CICY3400

  • rank 1
  • ℤ₂
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
6
h2,1h^{2,1}
24
χ\chi
−36
ambient factors
6
polynomials
8
iso-flops
1
Coxeter rank
1
Coxeter group
ℤ₂
Configuration matrix
6×8 configuration
X3400=[P111000000P200210000P200101100P200010011P210001010P201000101]−366,24X_{3400} = \left[\begin{array}{c|cccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 2 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 \\ \mathbb{P}^{2} & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ \mathbb{P}^{2} & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 \end{array}\right]^{6,24}_{-36}
Second Chern class
c2(X)⋅Di=(243636363636)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 36 & 36 & 36 & 36 & 36 \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 2, Type 2
M^1=(1000000−10000011000020100000010000001)\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 3400, H11 -> 6, H21 -> 24, C2 -> {24, 36, 36, 36, 36, 36}, Conf -> {{1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 2, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 1}, {1, 0, 0, 0, 1, 0, 1, 0}, {0, 1, 0, 0, 0, 1, 0, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{2, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0}, {0, 2, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}}}, CoxeterMat -> {{1}}|>
Plain text 
Num           : 3400
H11           : 6
H21           : 24
C2            : {24, 36, 36, 36, 36, 36}
Conf          : {{1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 2, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 1}, {1, 0, 0, 0, 1, 0, 1, 0}, {0, 1, 0, 0, 0, 1, 0, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{2, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0}, {0, 2, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}}}
CoxeterMat    : {{1}}