# Difference equation for quintic 3-fold.

@article{Wen2020DifferenceEF, title={Difference equation for quintic 3-fold.}, author={Yaoxiong Wen}, journal={arXiv: Algebraic Geometry}, year={2020} }

In this paper, we use the Mellin-Barnes method to relate solutions of certain type difference equations at $Q=0$ and $Q=\infty$. Then, we consider two special cases; one is the difference equation of $K$-theoretic $I$-function of the quintic, which is of degree 25; we use Adam's method to find the extra 20 solutions at $Q=0$. Another example is a Fuchsian case, which is confluent to the differential equation of cohomological $I$-function of the quintic. We compute the connection matrix and… Expand

#### 3 Citations

On the quantum K-theory of the quintic

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Quantum K-theory of a smooth projective variety at genus zero is a collection of integers that can be assembled into a generating series J(Q, q, t) that satisfies a system of linear differential… Expand

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This is a set of lecture notes for the first author’s lectures on the difference equations in 2019 at the Institute of Advanced Study for Mathematics at Zhejiang University. We focus on explicit… Expand

Confluence in quantum K-theory of weak Fano manifolds and q-oscillatory integrals for toric manifolds

- Mathematics
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For a smooth projective variety whose anti-canonical bundle is nef, we prove confluence of the small K-theoretic J-function, i.e., after rescaling appropriately the Novikov variables, the small… Expand

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This is a set of lecture notes for the first author’s lectures on the difference equations in 2019 at the Institute of Advanced Study for Mathematics at Zhejiang University. We focus on explicit… Expand

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