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arXiv · 2011.07527

Difference Equation for Quintic 3-Fold

Yaoxiong Wen
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Abstract

In this paper, we use the Mellin-Barnes-Watson method to relate solutions of a certain type of $q$-difference equations at $Q=0$ and $Q=\infty$. We consider two special cases; the first is the $q$-difference equation of $K$-theoretic $I$-function of the quintic, which is degree 25; we use Adams' method to find the extra 20 solutions at $Q=0$. The second special case is a fuchsian case, which is confluent to the differential equation of the cohomological $I$-function of the quintic. We compute the connection matrix and study the confluence of the $q$-difference structure.

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Yaoxiong Wen. 2020-11-15. Difference Equation for Quintic 3-Fold. https://doi.org/10.3842/sigma.2022.043

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