arXiv subjects
Publications and source records attributed to David Villalobos-Paz.
We prove that the automorphism group of an affine, cubic surface with equation $xyz=g(x,y)$ contains ${\mathbb Z}$ as a finite index subgroup. These equations were first studied by Mordell. v.2: small changes, references updated.
We show that a smooth Moishezon space $Y$ is non-projective if and only if it contains a rational curve such that $-[C] \in \overline{\mathrm{NE}}(Y)$. More generally, this holds if $Y$ has $\mathbb{Q}$-factorial, log terminal singularities. We derive this as a consequence of our main technical result: that we can run the relative minimal model program when the base is a normal algebraic space $Y$ of finite type over a field of characteristic $0$. As a second application, we show that every log canonical pair $(Y, Δ)$, where $Y$ is an algebraic space of finite type over a field of characteristic $0$ admits a dlt modification that is projective over $Y$.
We give a short proof of a Grothendieck-Lefschetz Theorem for equivariant Picard groups of nonsingular varieties with the action of an affine algebraic group.