Calabi-Yau differential operator database v.3.0

Summary

You searched for: c2h=38

Your search produced exactly one match

New Number: 3.14 | AESZ: | Superseeker: 444 19050964 | Hash: dc96aa2da269d989ee90c49dab6a9c5a

Degree: 3

\(\theta^4-2^{2} x\left(452\theta^4+920\theta^3+633\theta^2+173\theta+17\right)-2^{4} x^{2}(4\theta+3)(3808\theta^3+10504\theta^2+8884\theta+1635)-2^{8} 11^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)\)

Maple LaTex

Coefficients of the holomorphic solution: 1, 68, 42220, 38866320, 43812369900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 444, 57104, 19050964, 9432910668, 5781274591408, ... ; Common denominator:...

Discriminant

\(-(1936z-1)(1+64z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\) \(0\) \(\frac{ 1}{ 1936}\) \(\infty\)
\(0\) \(0\) \(0\) \(\frac{ 1}{ 4}\)
\(\frac{ 1}{ 2}\) \(0\) \(1\) \(\frac{ 3}{ 4}\)
\(1\) \(0\) \(1\) \(\frac{ 7}{ 4}\)
\(\frac{ 3}{ 2}\) \(0\) \(2\) \(\frac{ 9}{ 4}\)

\(-\frac{ 1}{ 64}\)	\(0\)	\(\frac{ 1}{ 1936}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(\frac{ 1}{ 2}\)	\(0\)	\(1\)	\(\frac{ 3}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 7}{ 4}\)
\(\frac{ 3}{ 2}\)	\(0\)	\(2\)	\(\frac{ 9}{ 4}\)

Note:

This is operator Pi = 3.14 (approx.), equivalent to AESZ 238.

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

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

\(-100\lambda\)	\(\frac{ 29}{ 12}\)	\(1\)	\(1\)
\(-\frac{ 19}{ 12}\)	\(-\frac{ 5}{ 2}\)	\(-1\)	\(0\)
\(0\)	\(5\)	\(0\)	\(0\)
\(-5\)	\(0\)	\(0\)	\(0\)