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ADDENDUM TO “HILBERT SQUARES OF K3 SURFACES AND DEBARRE-VOISIN VARIETIES”

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ADDENDUM TO “HILBERT SQUARES OF K3 SURFACES AND DEBARRE-VOISIN VARIETIES”

OLIVIER DEBARRE

There is an error in [DHOV, Table 2]: the entry 15 should be 4. Consequently, the divisors D2, D6, D8, D10, and D18 are expected to be HLS divisors. This was recently proved in [O, Corollary 1], together with the fact thatD30isnotan HLS divisor, answering a question raised in the introduction of [DHOV]. It remains to understand the geometry of the HLS divisor D8.

References

[DHOV] Debarre, O., Han, F., O’Grady, K., Voisin, C., Hilbert squares of K3 surfaces and Debarre-Voisin varieties,J. ´Ec. polytech. Math. 7(2020), 653–710.

[O] Oberdieck, G., Gromov–Witten theory and Noether–Lefschetz theory for holomorphic-symplectic va- rieties, eprintarXiv:2102.11622.

Universit´e de Paris, CNRS, IMJ-PRG, F-75013 Paris, France E-mail address: [email protected]

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