A tropical view on Landau-Ginzburg models
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913238824779776 |
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| author | Carl, Michael Pumperla, Max Siebert, Bernd |
| author_facet | Carl, Michael Pumperla, Max Siebert, Bernd |
| contents | This paper, largely written in 2009/2010, fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001. This point of view transparently brings in tropical disks of Maslov index 2 via the notion of broken lines, previously introduced in two dimensions by Mark Gross in his study of mirror symmetry for $\mathbb{P}^2$.
A major insight is the equivalence of properness of the Landau-Ginzburg potential with smoothness of the anticanonical divisor on the mirror side. We obtain proper superpotentials which agree on an open part with those classically known for toric varieties. Examples include mirror LG models for non-singular and singular del Pezzo surfaces, Hirzebruch surfaces and some Fano threefolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_07753 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A tropical view on Landau-Ginzburg models Carl, Michael Pumperla, Max Siebert, Bernd Algebraic Geometry 14J33, 14T05 This paper, largely written in 2009/2010, fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001. This point of view transparently brings in tropical disks of Maslov index 2 via the notion of broken lines, previously introduced in two dimensions by Mark Gross in his study of mirror symmetry for $\mathbb{P}^2$. A major insight is the equivalence of properness of the Landau-Ginzburg potential with smoothness of the anticanonical divisor on the mirror side. We obtain proper superpotentials which agree on an open part with those classically known for toric varieties. Examples include mirror LG models for non-singular and singular del Pezzo surfaces, Hirzebruch surfaces and some Fano threefolds. |
| title | A tropical view on Landau-Ginzburg models |
| topic | Algebraic Geometry 14J33, 14T05 |
| url | https://arxiv.org/abs/2205.07753 |