Period integrals and mutation

Tveiten, Ketil

doi:10.1090/tran/7320

Period integrals and mutation
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Trans. Amer. Math. Soc. 370 (2018), 8377-8401 Request permission

Abstract:

We define what it means for a Laurent polynomial in two variables to be mutable. For a mutable Laurent polynomial we prove several results about $f$ and its period $\pi _f$ in terms of the Newton polygon of $f$. In particular, we give an in principle complete description of the monodromy of $\pi _f$ around the origin. Special attention is given to the class of maximally mutable Laurent polynomials, which has applications to the conjectured classification of Fano manifolds via mirror symmetry.

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