Calabi-Yau differential operator database v.3.0

1

New Number: 2.62 | AESZ: 28 | Superseeker: 5 312 | Hash: 06dd455cafc5097e4f671d385984c1a2

Degree: 2

$\theta^4-x\left(65\theta^4+130\theta^3+105\theta^2+40\theta+6\right)+2^{2} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)$

Coefficients of the holomorphic solution: 1, 6, 126, 3948, 149310, ...
--> OEIS
Normalized instanton numbers (n₀=1): 5, 28, 312, 4808, 91048, ... ; Common denominator:...

Discriminant

$(64z-1)(z-1)$

Local exponents

$0$ $\frac{ 1}{ 64}$ $1$ $\infty$
$0$ $0$ $0$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 5}{ 4}$

\(0\)	\(\frac{ 1}{ 64}\)	\(1\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(2\)	\(\frac{ 5}{ 4}\)

Note:

A-incarnation: $X(1, 1, 1, 1, 1, 1) \subset Grass(3, 6)$

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-96\)	\(84\)	\(42\)	\(14\)

2

New Number: 2.64 | AESZ: 182 | Superseeker: 1 7 | Hash: 89ba4729efa82413b33fe6928ff8d2c9

Degree: 2

$\theta^4-x\left(43\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+2^{2} 3 x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6, 66, 924, 14850, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1, 7/4, 7, 40, 270, ... ; Common denominator:...

Discriminant

$(27z-1)(16z-1)$

Local exponents

$0$ $\frac{ 1}{ 27}$ $\frac{ 1}{ 16}$ $\infty$
$0$ $0$ $0$ $\frac{ 5}{ 6}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 7}{ 6}$

\(0\)	\(\frac{ 1}{ 27}\)	\(\frac{ 1}{ 16}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 5}{ 6}\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(2\)	\(\frac{ 7}{ 6}\)

Note:

This is operator "2.64" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-96\)	\(132\)	\(132\)	\(33\)

3

New Number: 5.82 | AESZ: 313 | Superseeker: 45 43531 | Hash: f8bfe82988e14680bdb775a3ce956216

Degree: 5

$\theta^4-x(\theta+1)(285\theta^3+321\theta^2+128\theta+18)-2 x^{2}\left(1640\theta^4+1322\theta^3-1337\theta^2-1178\theta-240\right)-2^{2} 3^{2} x^{3}\left(213\theta^4-256\theta^3-286\theta^2-80\theta-5\right)+2^{3} 3^{3} x^{4}(2\theta+1)(22\theta^3+37\theta^2+24\theta+6)+2^{4} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 18, 1662, 236340, 40943070, ...
--> OEIS
Normalized instanton numbers (n₀=1): 45, 845, 43531, 3091112, 273471538, ... ; Common denominator:...

Discriminant

$(z-1)(48z^2+296z-1)(6z+1)^2$

Local exponents

$-\frac{ 37}{ 12}-\frac{ 7}{ 6}\sqrt{ 7}$ $-\frac{ 1}{ 6}$ $0$ $-\frac{ 37}{ 12}+\frac{ 7}{ 6}\sqrt{ 7}$ $1$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $3$ $0$ $1$ $1$ $1$
$2$ $4$ $0$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 37}{ 12}-\frac{ 7}{ 6}\sqrt{ 7}\)	\(-\frac{ 1}{ 6}\)	\(0\)	\(-\frac{ 37}{ 12}+\frac{ 7}{ 6}\sqrt{ 7}\)	\(1\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(1\)
\(2\)	\(4\)	\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.82" from ...

\(16.+8.373926794I\)	\(-5-576\lambda\)	\(\frac{ 5}{ 4}+144\lambda\)	\(-.204864220-.332298682I\)
\(63\)	\(-20\)	\(\frac{ 21}{ 4}\)	\(-\frac{ 5}{ 4}-144\lambda\)
\(252\)	\(-84\)	\(22\)	\(-5-576\lambda\)
\(756+\frac{ 1}{ 500000000}I\)	\(-252\)	\(63\)	\(-14.-8.373926794I\)

\(\frac{ 17}{ 4}+288\lambda\)	\(-\frac{ 13}{ 24}-48\lambda\)	\(\frac{ 13}{ 96}+12\lambda\)	\(-.21754163e-1-\frac{ 52}{ 11}\lambda\)
\(\frac{ 33}{ 2}\)	\(-\frac{ 7}{ 4}\)	\(\frac{ 11}{ 16}\)	\(-\frac{ 13}{ 96}-12\lambda\)
\(66\)	\(-11\)	\(\frac{ 15}{ 4}\)	\(-\frac{ 13}{ 24}-48\lambda\)
\(396\)	\(-66\)	\(\frac{ 33}{ 2}\)	\(-\frac{ 9}{ 4}-288\lambda\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

\(1\)	\(-1\)	\(\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(-1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(0\)	\(1\)	\(-1\)
\(0\)	\(0\)	\(0\)	\(1\)

\(1+96\lambda\)	\(0\)	\(8\lambda\)	\(.5153046e-2\)
\(\frac{ 7}{ 2}\)	\(1\)	\(\frac{ 7}{ 24}\)	\(-8\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(42\)	\(0\)	\(\frac{ 7}{ 2}\)	\(1-96\lambda\)

\(-96\lambda\)	\(\frac{ 21}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 7}{ 2}\)	\(-21\)	\(-1\)	\(0\)
\(0\)	\(42\)	\(0\)	\(0\)
\(-42\)	\(0\)	\(0\)	\(0\)

\(1+96\lambda\)	\(0\)	\(4\lambda\)	\(.1639606e-2\)
\(\frac{ 11}{ 2}\)	\(1\)	\(\frac{ 11}{ 48}\)	\(-4\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(132\)	\(0\)	\(\frac{ 11}{ 2}\)	\(1-96\lambda\)

\(-96\lambda\)	\(\frac{ 55}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 11}{ 2}\)	\(-66\)	\(-1\)	\(0\)
\(0\)	\(132\)	\(0\)	\(0\)
\(-132\)	\(0\)	\(0\)	\(0\)