6 problems

Let $A$ be a Gorenstein local algebra of dimension $n+1$ with maximal ideal $\mathfrak{m}$, and let $U$ be a hyperplane in $\mathfrak{m}$ complementary to $\operatorname{Soc} A$. B…

Let $A$ be a Gorenstein local algebra of dimension $n+1$ with maximal ideal $\mathfrak{m}$, and let $U\subseteq\mathfrak{m}$ be a hyperplane complementary to $\operatorname{Soc} A$…

Additive-action multiplicity conjecture. There are at least two non-equivalent induced additive actions on $X$.

Let $X$ be a smooth Fano variety of Picard number one that is an equivariant compactification of a vector group. Euler-symmetric embedding conjecture. There is a suitable projectiv…

Let $X\subseteq\mathbb{P}^{n+1}$ be a degenerate hypersurface admitting an induced additive action, where an induced additive action is an additive action obtained from the ambient…

An Euler-symmetric variety is a variety such that, for a generic point $P$, there is a one-dimensional torus $\mathbb{G}_m$ in its automorphism group for which $P$ is an isolated f…