On the uniruled Voisin divisor on the LLSvS variety

Abstract

Let $Y$ be a smooth cubic fourfold, $F$ be its Fano variety of lines and $Z$ be its associated LLSvS variety, parametrizing families of twisted cubics and some of their degenerations. In this short note, we show that the divisor of singular cubic surfaces on $Z$ has two irreducible components, one of which coincides with the uniruled branch divisor of a resolution of the Voisin map $F\times F \dashrightarrow Z$.