English

The indeterminacy locus of the Voisin map

Algebraic Geometry 2024-08-02 v4

Abstract

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

Keywords

Cite

@article{arxiv.1711.06218,
  title  = {The indeterminacy locus of the Voisin map},
  author = {Giosuè Emanuele Muratore},
  journal= {arXiv preprint arXiv:1711.06218},
  year   = {2024}
}

Comments

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