Self-dual projective toric varieties

Let T be a torus over an algebraically closed field k of characteristic 0, and consider a projective T-module P(V). We determine when a projective toric subvariety X of P(V) is self-dual, in terms of the configuration of weights of V.Comment: 26 pages, 1 figure. Minor change

On the orbits of plane automorphisms and their stabilizers

Let $\Bbbk$ be a perfect field with algebraic closure $\overline{\Bbbk}$. If $H$ is a subgroup of plane automorphisms over $\Bbbk$ and $p\in\overline{\Bbbk}^2$ is a point, we describe the subgroup consisting of plane automorphisms which stabilize the orbit of $p$ under $H$, when this orbit has irreducible closure in $\overline{\Bbbk}^2$. As an application, we treat the case where $H$ is cyclic and the closure of the orbit of $p$ is an arbitrary (non-necessarily irreducible) curve.Comment: 14 page