Hodge diamonds of the Landau--Ginzburg orbifolds

Author:

Alexey Basalaev, Andrei Ionov

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Mathematical Physics (math-ph)

journal:

date:

2023-07-02 16:00:00

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 necessarily abelian. Assume further that $G$ contains the grading operator $j_f$ and $f$ satisfies the Calabi-Yau condition. We prove that the nonvanishing bi-graded pieces of the B--model state space of $(f,G)$ form a diamond. We identify its top-most, bottom-most, left-most and right-most entries as one-dimensional and show that this diamond enjoys the essential horizontal and vertical isomorphisms.

PDF: Hodge diamonds of the Landau--Ginzburg orbifolds.pdf