Conference abstracts

Session S10 - Homological Methods

July 28, 17:30 ~ 18:00

## Title: Invariant theory of Milnor algebras

### Australian National University, Australia   -   jarod.alper@anu.edu.au

Given a non-degenerate homogeneous form $f$ on $\mathbb{C}^n$ of degree $d$, the Milnor algebra of $f$ is defined as the quotient of the polynomial ring $\mathbb{C}[x_1, ..., x_n]$ by the ideal $J(f)$ of first order partials of $f$. For each integer $k$, one can define the $k$th Hilbert point of the Milnor algebra as the subspace of degree $k$ polynomials contained in $J(f)$. When $k=n(d-2)$, this Hilbert point is classically called a Macaulay inverse system. We study the invariant theory of the these Hilbert points viewed as points in the corresponding Grassmanians. We will then be able to resolve a conjecture of Eastwood and Isaev which is related to the well-known Mather-Yau theorem for isolated hypersurface singularities.

Joint work with Alex Isaev (Australian National University) and Maksym Fedorchuk (Boston College).