arXiv subjects
Publications and source records attributed to Sione Ma'u.
We classify pairs $(X,G)$ consisting of a (possibly singular) cubic threefold $X\subset\mathbb{P}^4$ and a finite subgroup $G\subset\mathrm{Aut}(X)$ such that $X$ is $G$-birationally rigid, i.e., $X$ is a $G$-Mori fiber space (over a point), and $X$ is not $G$-birational to any $G$-Mori fibre space that is not $G$-biregular to $X$.
In previous works, the second author defined directional Robin constants associated to a compact, nonpolar subset $K$ of an algebraic curve $A$ in $\mathbb{C}^N$ and related these to a natural class of Chebyshev constants for $K$. We define a second class of Chebyshev constants for $K$; relate these two classes; and utilize each of them to define two families of extremal-like functions which can be used to recover the Siciak-Zaharjuta extremal function for $K$.
We study Fano threefolds that can be obtained by blowing up the three-dimensional projective space along a smooth curve of degree six and genus three. We produce many new K-stable examples of such threefolds, and we describe all finite groups that can act faithfully on them.
We introduce explicit families of good interpolation points for interpolation on a triangle in $\mathbb{R}^2$ that may be used for either polynomial interpolation or a certain rational interpolation for which we give explicit formulas.
We show that the Monge-Ampère density of the extremal function $V_P$ for a non-convex Pac-Man set $P\subset {\bf R}^2$ tends to a finite limit as we approach the vertex $p$ of $P$ linearly but with a value that may vary with the line. On the other hand, along a tangential approach to $p$ the Monge-Ampère density becomes unbounded. This partially mimics the behavior of the Monge-Ampère density of the union of two quarter disks set $S$ of Sigurdsson and Snaebjarnarson. We also recover their formula for $V_S$ by elementary methods.