• Corpus ID: 235422010

Divisors in the moduli space of Debarre-Voisin varieties

  title={Divisors in the moduli space of Debarre-Voisin varieties},
  author={Vladimiro Benedetti and Jieao Song},
Let V10 be a 10-dimensional complex vector space and let σ ∈ ∧ V ∨ 10 be a non-zero alternating 3-form. One can define several associated degeneracy loci: the Debarre– Voisin variety X 6 ⊂ Gr(6, V10), the Peskine variety X 1 ⊂ P(V10), and the hyperplane section X 3 ⊂ Gr(3, V10). Their interest stems from the fact that the Debarre–Voisin varieties form a locally complete family of projective hyperkähler fourfolds of K3-type. We prove that when smooth, the varieties X 6 , X 1 , and X 3 share one… 

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