The indeterminacy locus of the Voisin map

Abstract

Beauville and Donagi proved that the variety of lines $F(Y)$ of a smooth cubic fourfold $Y$ is a hyperkähler variety. Recently, C. Lehn, M.Lehn, Sorger and van Straten proved that one can naturally associate a hyperKähler variety $Z(Y)$ to the variety of twisted cubics on $Y$. Then, Voisin defined a degree 6 rational map $\psi :F(Y)\times F(Y)⇢Z(Y)$. We will show that the indeterminacy locus of $\psi$ is the locus of intersecting lines.

15 pages. Typo in proposition 2.2. Introduced Remark 2.3. Chages in reference LLSvS17. Insered $W_{ADE}$ and removed the explanation of $\varphi$ Definition of ${\psi }^{\prime }$ using the Rigidity Lemma. E is now the support of the exceptional divisor

References in corpus (1)

• On the symplectic eightfold associated to a Pfaffian cubic fourfold