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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Period integrals and mutation


Author: Ketil Tveiten
Journal: Trans. Amer. Math. Soc. 370 (2018), 8377-8401
MSC (2010): Primary 32S40, 14J33
DOI: https://doi.org/10.1090/tran/7320
Published electronically: July 5, 2018
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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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Additional Information

Ketil Tveiten
Affiliation: Department of Mathematics Uppsala University Box 256 75105 Uppsala Sweden
Email: ketiltveiten@gmail.com

DOI: https://doi.org/10.1090/tran/7320
Keywords: Monodromy, periods, mirror symmetry
Received by editor(s): March 3, 2015
Received by editor(s) in revised form: October 13, 2015, April 22, 2016, and March 17, 2017
Published electronically: July 5, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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