CICY Coxeter DB | 5305

CICY5305

  • rank 2
  • I₂(2)
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
4
h2,1h^{2,1}
28
χ\chi
−48
ambient factors
4
polynomials
5
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(2)
Configuration matrix
4×5 configuration
X5305=[P221000P210110P201101P200012]−484,28X_{5305} = \left[\begin{array}{c|ccccc} \mathbb{P}^{2} & 2 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{2} & 1 & 0 & 1 & 1 & 0 \\ \mathbb{P}^{2} & 0 & 1 & 1 & 0 & 1 \\ \mathbb{P}^{2} & 0 & 0 & 0 & 1 & 2 \end{array}\right]^{4,28}_{-48}
Second Chern class
c2(X)⋅Di=(36363636)Tc_2(X)\cdot D_i = \begin{pmatrix} 36 & 36 & 36 & 36 \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 2
M^1=(−1000110020100001)\hat{M}_1 = \begin{pmatrix} -1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 2 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 4, Type 2
M^2=(100001020011000−1)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & -1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 5305, H11 -> 4, H21 -> 28, C2 -> {36, 36, 36, 36}, Conf -> {{2, 1, 0, 0, 0}, {1, 0, 1, 1, 0}, {0, 1, 1, 0, 1}, {0, 0, 0, 1, 2}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 2"}, {4, "Type 2"}}, KahlerRefGens -> {{{-1, 0, 0, 0}, {1, 1, 0, 0}, {2, 0, 1, 0}, {0, 0, 0, 1}}, {{1, 0, 0, 0}, {0, 1, 0, 2}, {0, 0, 1, 1}, {0, 0, 0, -1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>
Plain text 
Num           : 5305
H11           : 4
H21           : 28
C2            : {36, 36, 36, 36}
Conf          : {{2, 1, 0, 0, 0}, {1, 0, 1, 1, 0}, {0, 1, 1, 0, 1}, {0, 0, 0, 1, 2}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 2"}, {4, "Type 2"}}
KahlerRefGens : {{{-1, 0, 0, 0}, {1, 1, 0, 0}, {2, 0, 1, 0}, {0, 0, 0, 1}}, {{1, 0, 0, 0}, {0, 1, 0, 2}, {0, 0, 1, 1}, {0, 0, 0, -1}}}
CoxeterMat    : {{1, 2}, {2, 1}}