Sangho Byun | Searcharxiv

arXiv2015

Stability of nets of quadrics in $\mathbb{P}^5$ and associated discriminants

Let $S$ be a complete intersection surface defined by a net $Λ$ of quadrics in $\mathbb P^5$. In this paper we analyze GIT stability of nets of quadrics in $\mathbb P^5$ up to projective equivalence, and discuss some connections between a net of quadrics and the associated discriminant sextic curve. In particular, we prove that if $S$ is normal and the discriminant $Δ(S)$ of $S$ is stable then $Λ$ is stable. And we prove that if $S$ has the reduced discriminant and $Δ(S)$ is stable then $Λ$ is stable. Moreover, we prove that if $S$ has simple singularities then $Δ(S)$ has simple singularities.

math.AG↗

arXiv2014

Stability of hypersurface sections of quadric threefolds

Let $S$ be a complete intersection of a smooth quadric 3-fold $Q$ and a hypersurface of degree $d$ in ${\mathbb P}^4$. In this paper we analyze GIT stability of $S$ with respect to the natural $G=SO(5, {\mathbb C})$-action. We prove that if $d\ge 4$ and $S$ has at worst semi-log canonical singularities then $S$ is $G$-stable. Also, we prove that if $d\ge 3$ and $S$ has at worst semi-log canonical singularities then $S$ is $G$-semistable.

math.AG↗