Orbifold Milnor lattice and orbifold intersection form

TL;DR

This paper extends the classical concepts of Milnor lattice and intersection form to orbifold settings in quantum singularity theory, introducing orbifold monodromy, Seifert forms, and symmetry properties for invertible polynomials.

Contribution

It defines orbifold versions of key invariants like monodromy, Milnor lattice, and intersection form, advancing the understanding of orbifold quantum cohomology in singularity theory.

Findings

Defined orbifold monodromy operator and orbifold Milnor lattice

Described symmetry properties of invariants of invertible polynomials

Refined known invariants with new symmetry insights

Abstract

For a germ of a quasihomogeneous function with an isolated critical point at the origin invariant with respect to an appropriate action of a finite abelian group, H. Fan, T. Jarvis, and Y. Ruan defined the so-called quantum cohomology group. It is considered as the main object of the quantum singularity theory (FJRW-theory). We define orbifold versions of the monodromy operator on the quantum (co)homology group, of the Milnor lattice, of the Seifert form and of the intersection form. We also describe some symmetry properties of invariants of invertible polynomials refining the known ones.