Orbifold Jacobian Algebras and Orbifold Euler Characteristics

Let f be a quasihomogeneous polynomial with an isolated singularity at the origin. The Jacobian algebra of f is the local algebra of its partial derivatives. It is finite dimensional and has the structure of a Frobenius algebra. Its dimension is related to the Euler characteristic of the Milnor fibre of f. We consider a group action on f. Let G be a finite group of symmetries of f. The pair (f,G) is often called a Landau-Ginzburg orbifold. We construct an orbifold version of the Jacobian algebra and relate it to notions of orbifold Euler characteristics for the pair (f,G).