Journal article
Tropical Superpotential for $\mathbb{P}^2$
- Abstract:
- We present an extended worked example of the computation of the tropical superpotential considered by Carl–Pumperla–Siebert. In particular we consider an affine manifold associated to the complement of a non-singular genus one plane curve and calculate the wall and chamber decomposition determined by the Gross–Siebert algorithm. Using the results of Carl–Pumperla–Siebert we determine the tropical superpotential, via broken line counts, in every chamber of this decomposition. The superpotential defines a Laurent polynomial in every chamber, and we show that these are precisely the Laurent polynomials predicted by Coates–Corti–Galkin–Golyshev–Kaspzryk to be mirror to $\mathbb{P}^2$.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 606.3KB, Terms of use)
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- Publisher copy:
- 10.14231/AG-2020-002
Authors
+ Engineering and Physical Sciences Research Council
More from this funder
- Funding agency for:
- Prince, T
- Publisher:
- Foundation Compositio Mathematica
- Journal:
- Algebraic Geometry More from this journal
- Volume:
- 7
- Issue:
- 1
- Pages:
- 30-58
- Publication date:
- 2019-11-13
- Acceptance date:
- 2019-02-09
- DOI:
- Keywords:
- Pubs id:
-
pubs:969925
- UUID:
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uuid:c7870b50-9145-4d1c-adf5-c2b577acb780
- Local pid:
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pubs:969925
- Source identifiers:
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969925
- Deposit date:
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2019-02-11
Terms of use
- Copyright date:
- 2019
- Notes:
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© Foundation Compositio Mathematica 2020. This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse,
distribution, and reproduction in any medium, provided that the original work is properly cited.
- Licence:
- CC Attribution (CC BY)
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