Hodge diamonds of the Landau--Ginzburg orbifolds

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 $\mathrm{SL}(N,\mathbb{C})$, 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.

References in corpus (2)

• FJRW rings and Landau-Ginzburg Mirror Symmetry
• Mirror map for Fermat polynomial with non-abelian group of symmetries