The minimal fibering degree of a toric variety equals the lattice width of its polytope
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- by Audric Lebovitz and David Stapleton;
- Trans. Amer. Math. Soc. 378 (2025), 3653-3665
- DOI: https://doi.org/10.1090/tran/9381
- Published electronically: March 5, 2025
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Abstract:
The purpose of this paper is to compute the minimal fibering degree of an arbitrary projective toric variety. We prove that it equals the lattice width of the associated polytope. This gives a complete answer to a question asked in a recent paper of Levinson, Ullery and the second author. The minimal fibering degree of a polarized projective variety was introduced in that paper in order to compute the degree of irrationality (a generalization of gonality) of high degree divisors. From this perspective, our paper gives a higher dimensional analogue of results of Kawaguchi and others who computed the gonality of curves in toric surfaces in terms of lattice widths.References
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Bibliographic Information
- Audric Lebovitz
- Affiliation: Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, California 90095.
- MR Author ID: 1548074
- Email: alebovit@math.ucla.edu
- David Stapleton
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
- MR Author ID: 1176826
- ORCID: 0000-0002-0142-3211
- Email: dajost@umich.edu
- Received by editor(s): August 8, 2023
- Received by editor(s) in revised form: November 4, 2024
- Published electronically: March 5, 2025
- Additional Notes: During the preparation of this article, the second author was partially supported by NSF grant FRG-1952399.
- © Copyright 2025 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 3653-3665
- MSC (2020): Primary 14M25, 14D06
- DOI: https://doi.org/10.1090/tran/9381