Hodge diamonds of the Landau--Ginzburg orbifolds
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929286831669248 |
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| author | Basalaev, Alexey Ionov, Andrei |
| author_facet | Basalaev, Alexey Ionov, Andrei |
| contents | Consider the pairs $(f,G)$ with $f = f(x_1,\dots,x_N)$ being a polynomial defining a quasihomogeneous singularity and $G$ being a subgroup of ${\rm SL}(N,\mathbb{C})$, preserving $f$. In particular, $G$ is not necessary abelian. Assume further that $G$ contains the grading operator $j_f$ and $f$ satisfies the Calabi-Yau condition. We prove that the nonvanishing bigraded pieces of the B-model state space of $(f,G)$ form a diamond. We identify its topmost, bottommost, leftmost and rightmost entries as one-dimensional and show that this diamond enjoys the essential horizontal and vertical isomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01295 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hodge diamonds of the Landau--Ginzburg orbifolds Basalaev, Alexey Ionov, Andrei Algebraic Geometry Mathematical Physics Consider the pairs $(f,G)$ with $f = f(x_1,\dots,x_N)$ being a polynomial defining a quasihomogeneous singularity and $G$ being a subgroup of ${\rm SL}(N,\mathbb{C})$, preserving $f$. In particular, $G$ is not necessary abelian. Assume further that $G$ contains the grading operator $j_f$ and $f$ satisfies the Calabi-Yau condition. We prove that the nonvanishing bigraded pieces of the B-model state space of $(f,G)$ form a diamond. We identify its topmost, bottommost, leftmost and rightmost entries as one-dimensional and show that this diamond enjoys the essential horizontal and vertical isomorphisms. |
| title | Hodge diamonds of the Landau--Ginzburg orbifolds |
| topic | Algebraic Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2307.01295 |