CICY Coxeter DB | 4899

CICY4899

  • rank 1
  • ℤ₂
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
7
h2,1h^{2,1}
29
χ\chi
−44
ambient factors
7
polynomials
7
iso-flops
1
Coxeter rank
1
Coxeter group
ℤ₂
Configuration matrix
7×7 configuration
X4899=[P11100000P10010100P10001010P11000010P20101001P22000100P20010011]−447,29X_{4899} = \left[\begin{array}{c|ccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ \mathbb{P}^{1} & 1 & 0 & 0 & 0 & 0 & 1 & 0 \\ \mathbb{P}^{2} & 0 & 1 & 0 & 1 & 0 & 0 & 1 \\ \mathbb{P}^{2} & 2 & 0 & 0 & 0 & 1 & 0 & 0 \\ \mathbb{P}^{2} & 0 & 0 & 1 & 0 & 0 & 1 & 1 \end{array}\right]^{7,29}_{-44}
Second Chern class
c2(X)⋅Di=(24242424363636)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 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 6, Type 2
M^1=(1000010010002000100000001010000010000000−100000001)\hat{M}_1 = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 2 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 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 -> 4899, H11 -> 7, H21 -> 29, C2 -> {24, 24, 24, 24, 36, 36, 36}, Conf -> {{1, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 1, 0}, {1, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 1, 0, 0, 1}, {2, 0, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 1, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{6, "Type 2"}}, KahlerRefGens -> {{{1, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 2, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 1, 0}, {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           : 4899
H11           : 7
H21           : 29
C2            : {24, 24, 24, 24, 36, 36, 36}
Conf          : {{1, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 1, 0}, {1, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 1, 0, 0, 1}, {2, 0, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 1, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{6, "Type 2"}}
KahlerRefGens : {{{1, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 2, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 1, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 0, 1}}}
CoxeterMat    : {{1}}