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The indeterminacy locus of the Voisin map

Giosuè Emanuele Muratore

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 $ψ:F(Y)\times F(Y)\dashrightarrow Z(Y)$. We will show that the indeterminacy locus of $ψ$ is the locus of intersecting lines.

The indeterminacy locus of the Voisin map

Abstract

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

Paper Structure

This paper contains 4 sections, 7 theorems, 46 equations.

Table of Contents

  1. Introduction
  2. General facts
  3. General facts about the LLSS variety
  4. The Voisin map

Key Result

Theorem 1.2

The indeterminacy locus of the Voisin map $\psi:F(Y)\times F(Y)\dashrightarrow Z(Y)$ is the variety $I$ of intersecting lines in $Y$.

Theorems & Definitions (21)

  • Conjecture 1.1: MR2187148
  • Theorem 1.2
  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Proposition 2.4
  • proof
  • ...and 11 more