Period integrals and mutation

2015/01/21 by Ketil Tveiten, Tveiten, Ketil · 1 citation
Mathematics · #14F10 #14J33 #14J45 #32S40 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14F10 #msc:14J33 #msc:14J45 #msc:32S40

paper · pdf · doi:10.48550/arxiv.1501.05095

29 pages, 8 figures

arxiv created 2015/01/23 · arxiv updated 2015/01/26

Abstract

Let f be a Laurent polynomial in two variables, whose Newton polygon strictly contains the origin and whose vertices are primitive lattice points, and let L_f be the minimal-order differential operator that annihilates the period integral of f. We prove several results about f and L_f in terms of the Newton polygon of f and the combinatorial operation of *mutation*, in particular we give an in principle complete description of the monodromy of L_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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