Period integrals and mutation
(English)Manuscript (preprint) (Other academic)
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.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-116810OAI: oai:DiVA.org:su-116810DiVA: diva2:808335