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arXiv · 2307.01295

Hodge diamonds of the Landau--Ginzburg orbifolds

Alexey Basalaev·Andrei Ionov
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Abstract

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.

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Alexey Basalaev, Andrei Ionov. 2023-07-03. Hodge diamonds of the Landau--Ginzburg orbifolds. https://doi.org/10.3842/sigma.2024.024

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