CICY Coxeter DB | 4044

CICY4044

  • rank 1
  • ℤ₂
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
7
h2,1h^{2,1}
27
χ\chi
−40
ambient factors
7
polynomials
8
iso-flops
1
Coxeter rank
1
Coxeter group
ℤ₂
Configuration matrix
7×8 configuration
X4044=[P111000000P100101000P100010100P100000011P100000011P200110010P411001101]−407,27X_{4044} = \left[\begin{array}{c|cccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ \mathbb{P}^{2} & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ \mathbb{P}^{4} & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 \end{array}\right]^{7,27}_{-40}
Second Chern class
c2(X)⋅Di=(24242424243652)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 24 & 36 & 52 \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 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}

Database record

Mathematica 
<|Num -> 4044, H11 -> 7, H21 -> 27, C2 -> {24, 24, 24, 24, 24, 36, 52}, Conf -> {{1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, 0, 1, 1}, {0, 0, 1, 1, 0, 0, 1, 0}, {1, 1, 0, 0, 1, 1, 0, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 1a"}}, 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}}}, CoxeterMat -> {{1}}|>
Plain text 
Num           : 4044
H11           : 7
H21           : 27
C2            : {24, 24, 24, 24, 24, 36, 52}
Conf          : {{1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, 0, 1, 1}, {0, 0, 1, 1, 0, 0, 1, 0}, {1, 1, 0, 0, 1, 1, 0, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 1a"}}
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}}}
CoxeterMat    : {{1}}