CICY Coxeter DB | 7705

CICY7705

  • rank 2
  • I₂(∞) (P)
  • affine
Favorable Kähler-favProduct
h1,1h^{1,1}
5
h2,1h^{2,1}
53
χ\chi
−96
ambient factors
5
polynomials
6
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(∞) (P)
Configuration matrix
5×6 configuration
X7705=[P1110000P1001010P1000101P2001101P4110012]−965,53X_{7705} = \left[\begin{array}{c|cccccc} \mathbb{P}^{1} & 1 & 1 & 0 & 0 & 0 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 1 & 0 & 1 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 0 & 1 & 0 & 1 \\ \mathbb{P}^{2} & 0 & 0 & 1 & 1 & 0 & 1 \\ \mathbb{P}^{4} & 1 & 1 & 0 & 0 & 1 & 2 \end{array}\right]^{5,53}_{-96}
Second Chern class
c2(X)⋅Di=(2424243652)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 24 & 36 & 52 \end{pmatrix}^{T}
Coxeter diagram Gallery →
P
Coxeter matrixP, H=∞\text{P, H} = \infty
(1PP1)\begin{pmatrix} 1 & \text{P} \\ \text{P} & 1 \end{pmatrix}
Iso-flop reflections Kähler representation
M^1\hat{M}_1: row 1, Type 1a
M^1=(−1000001000001000001010001)\hat{M}_1 = \begin{pmatrix} -1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 5, Type 2
M^2=(100040100200101000110000−1)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 & 0 & 4 \\ 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & -1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 7705, H11 -> 5, H21 -> 53, C2 -> {24, 24, 24, 36, 52}, Conf -> {{1, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 1, 1, 0, 1}, {1, 1, 0, 0, 1, 2}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 1a"}, {5, "Type 2"}}, KahlerRefGens -> {{{-1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {1, 0, 0, 0, 1}}, {{1, 0, 0, 0, 4}, {0, 1, 0, 0, 2}, {0, 0, 1, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}}}, CoxeterMat -> {{1, P}, {P, 1}}|>
Plain text 
Num           : 7705
H11           : 5
H21           : 53
C2            : {24, 24, 24, 36, 52}
Conf          : {{1, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 1, 1, 0, 1}, {1, 1, 0, 0, 1, 2}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 1a"}, {5, "Type 2"}}
KahlerRefGens : {{{-1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {1, 0, 0, 0, 1}}, {{1, 0, 0, 0, 4}, {0, 1, 0, 0, 2}, {0, 0, 1, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}}}
CoxeterMat    : {{1, P}, {P, 1}}