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Birationality and Landau–Ginzburg Models

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Abstract

We introduce a new technique for approaching birationality questions that arise in the mirror symmetry of complete intersections in toric varieties. As an application we answer affirmatively and conclusively the question of Batyrev–Nill (Integer points in polyhedra—geometry, number theory, representation theory, algebra, optimization, statistics, volume 452 of Contemporary mathematics. American Mathematical Society, Providence, pp 35–66, 2008) about the birationality of Calabi–Yau families associated to multiple mirror nef-partitions. This completes the progress in this direction made by Li’s breakthrough (Li in Adv Math 299:71–107, 2016). In the process, we obtain results in the theory of Borisov’s nef-partitions (Borisov in Towards the mirror symmetry for Calabi–Yau complete intersections in Gorenstein toric Fano varieties, 1993. arXiv:alg-geom/9310001) and provide new insight into the geometric content of the multiple mirror phenomenon.

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  1. Department of Mathematics, Drexel University, Philadelphia, PA, 19104, USA

    Patrick Clarke

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  1. Patrick Clarke
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Correspondence to Patrick Clarke.

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Communicated by N. A. Nekrasov

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Clarke, P. Birationality and Landau–Ginzburg Models. Commun. Math. Phys. 353, 1241–1260 (2017). https://doi.org/10.1007/s00220-017-2830-0

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