arXiv subjects
Publications and source records attributed to Joseph Malbon.
We find all possible K-polystable degenerations of smooth K-polystable Fano threefolds in the family \textnumero2.21, and describe the component of the moduli space $M^\text{K-ps}_{3,28}$ which parametrises this family.
We prove that a faithful group action on the smooth complete intersection $X$ of three divisors of bidegree $(1,1)$ in $\p^3\times\p^3$ is linearisable if and only if $\rk(\pic^G(X))\ne1$.
Let $\mathcal F_{8,2\times\frac12(1,1,1)}$ be the moduli space of genus $8$ Fano $3$-folds with two terminal quotient singularities of type $\frac12(1,1,1)$. We prove that $\mathcal F_{8,2\times\frac12(1,1,1)}$ is rational. Moreover, we show that a general member of this family is K-stable.
We describe the automorphism groups of smooth Fano threefolds of rank 2 and degree 28 in the cases where they are finite.
We prove that all smooth Fano threefolds with Picard rank 2 and degree 28 are K-polystable, except for some explicit cases which we describe. We also give a classification of the normal bundle of a rational normal quartic curve in a smooth quadric threefold.