CICY Coxeter DB | 7780

CICY7780

  • rank 2
  • I₂(2)
  • finite
Favorable Kähler-favProduct
h1,1h^{1,1}
3
h2,1h^{2,1}
55
χ\chi
−104
ambient factors
3
polynomials
3
iso-flops
2
Coxeter rank
2
Coxeter group
I₂(2)
Configuration matrix
3×3 configuration
X7780=[P1110P1002P4221]−1043,55X_{7780} = \left[\begin{array}{c|ccc} \mathbb{P}^{1} & 1 & 1 & 0 \\ \mathbb{P}^{1} & 0 & 0 & 2 \\ \mathbb{P}^{4} & 2 & 2 & 1 \end{array}\right]^{3,55}_{-104}
Second Chern class
c2(X)⋅Di=(242456)Tc_2(X)\cdot D_i = \begin{pmatrix} 24 & 24 & 56 \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 1a
M^1=(−100010201)\hat{M}_1 = \begin{pmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 2 & 0 & 1 \end{pmatrix}
M^2\hat{M}_2: row 2, Type 2
M^2=(1000−10011)\hat{M}_2 = \begin{pmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 1 & 1 \end{pmatrix}

Database record

Mathematica 
<|Num -> 7780, H11 -> 3, H21 -> 55, C2 -> {24, 24, 56}, Conf -> {{1, 1, 0}, {0, 0, 2}, {2, 2, 1}}, Favour -> True, KahlerPos -> True, IsProduct -> False, IsoFlopRows -> {{1, "Type 1a"}, {2, "Type 2"}}, KahlerRefGens -> {{{-1, 0, 0}, {0, 1, 0}, {2, 0, 1}}, {{1, 0, 0}, {0, -1, 0}, {0, 1, 1}}}, CoxeterMat -> {{1, 2}, {2, 1}}|>
Plain text 
Num           : 7780
H11           : 3
H21           : 55
C2            : {24, 24, 56}
Conf          : {{1, 1, 0}, {0, 0, 2}, {2, 2, 1}}
Favour        : True
KahlerPos     : True
IsProduct     : False
IsoFlopRows   : {{1, "Type 1a"}, {2, "Type 2"}}
KahlerRefGens : {{{-1, 0, 0}, {0, 1, 0}, {2, 0, 1}}, {{1, 0, 0}, {0, -1, 0}, {0, 1, 1}}}
CoxeterMat    : {{1, 2}, {2, 1}}