On the Poincare polynomials for Landau-Ginzburg Orbifolds

TL;DR

This paper constructs Poincare polynomials for Landau-Ginzburg orbifolds, demonstrating dualities and deriving formulas for Hodge numbers in Calabi-Yau cases, advancing understanding of their topological invariants.

Contribution

It introduces a method to compute Poincare polynomials for Landau-Ginzburg orbifolds and derives explicit formulas for Hodge numbers in Calabi-Yau scenarios.

Findings

Dualities including Poincare duality are realized under certain conditions.

Explicit formulas for Hodge numbers $h^{2,1}$ and $h^{1,1}$ are obtained.

Poincare polynomials help understand topological invariants of Landau-Ginzburg orbifolds.

Abstract

We construct the Poincare polynomials for Landau-Ginzburg orbifolds with projection operators.Using them we show that special types of dualities including Poincare duality are realized under certain conditions. When Calabi-Yau interpretation exists, two simple formulae for Hodge numbers $h^{2,1}$ and $h^{1,1}$ are obtained.