CICY Coxeter DB | 5497

CICY5497

  • rank 1
  • ℤ₂
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
7
h2,1h^{2,1}
31
χ\chi
−48
ambient factors
7
polynomials
9
iso-flops
1
Coxeter rank
1
Coxeter group
ℤ₂
Configuration matrix
7×9 configuration
X5497=[P1110000000P1001001000P1000100100P1000010010P2100010001P2010100001P4011001110]−487,31X_{5497} = \left[\begin{array}{c|ccccccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ \mathbb{P}^{2} & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\ \mathbb{P}^{2} & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 \\ \mathbb{P}^{4} & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 \end{array}\right]^{7,31}_{-48}
Second Chern class
c2(X)⋅Di=(24242424363652)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 24 & 36 & 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 2, Type 1a
M^1=(10000000−10000000100000001000000010000000100100001)\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 \\ 0 & 1 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 5497, H11 -> 7, H21 -> 31, C2 -> {24, 24, 24, 24, 36, 36, 52}, Conf -> {{1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 0, 0, 0, 1}, {0, 1, 1, 0, 0, 1, 1, 1, 0}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{2, "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}, {0, 1, 0, 0, 0, 0, 1}}}, CoxeterMat -> {{1}}|>
Plain text 
Num           : 5497
H11           : 7
H21           : 31
C2            : {24, 24, 24, 24, 36, 36, 52}
Conf          : {{1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 0, 0, 0, 1}, {0, 1, 1, 0, 0, 1, 1, 1, 0}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{2, "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}, {0, 1, 0, 0, 0, 0, 1}}}
CoxeterMat    : {{1}}