On Arithmetic Mirror Symmetry for smooth Fano fourfolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914598685245440 |
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| author | Ovcharenko, Mikhail |
| author_facet | Ovcharenko, Mikhail |
| contents | We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in $n \leqslant 4$ variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, or are quiver flag zero loci. We discuss implications to Arithmetic Mirror Symmetry conjecture, a Hodge-theoretic approach to the study of Apéry constants of Fano varieties proposed by Golyshev--Kerr--Sasaki. Using the partial case of Arithmetic Mirror Symmetry conjecture proved by Kerr, we construct two examples of a Mirror Symmetry correspondence between specific algebraic classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26592 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Arithmetic Mirror Symmetry for smooth Fano fourfolds Ovcharenko, Mikhail Algebraic Geometry Number Theory 14J45, 14J32 We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in $n \leqslant 4$ variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, or are quiver flag zero loci. We discuss implications to Arithmetic Mirror Symmetry conjecture, a Hodge-theoretic approach to the study of Apéry constants of Fano varieties proposed by Golyshev--Kerr--Sasaki. Using the partial case of Arithmetic Mirror Symmetry conjecture proved by Kerr, we construct two examples of a Mirror Symmetry correspondence between specific algebraic classes. |
| title | On Arithmetic Mirror Symmetry for smooth Fano fourfolds |
| topic | Algebraic Geometry Number Theory 14J45, 14J32 |
| url | https://arxiv.org/abs/2604.26592 |