A special Debarre-Voisin fourfold

2021/06/24 by Song, Jieao · 1 citation
#14J35 #14J42 #14J50 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.13287

Abstract

Let \mathbf G be the finite simple group PSL(2,\mathbf F₁₁). It has an irreducible representation V₁₀ of dimension 10. In this note, we study a special trivector σ∈ \bigwedge³V₁₀^\vee which is \mathbf G-invariant. Following the construction of Debarre-Voisin, we obtain a smooth hyperkähler fourfold X₆^σ\subsetGr(6,V₁₀) with many symmetries. We will also look at the associated Peskine variety X₁^σ⊂ \mathbf P(V₁₀), which is highly symmetric as well and admits 55 isolated singular points. It will help us to understand better the geometry of the special Debarre-Voisin fourfold X₆^σ.

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• Peskine sixfolds and Debarre-Voisin fourfolds with associated cubic fourfolds

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