Geodesic
O’Grady tenfolds as moduli spaces of sheaves
Forum of Mathematics, Sigma, Tome 12 (2024)

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We give a lattice-theoretic characterization for a manifold of $\operatorname {\mathrm {OG10}}$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li–Pertusi–Zhao variety of $\operatorname {\mathrm {OG10}}$ type associated to any smooth cubic fourfold. Moreover, we determine when a birational transformation is induced by an automorphism of the K3 surface, and we use this to classify all induced birational symplectic involutions. 
@article{10_1017_fms_2024_46,
     author = {Camilla Felisetti and Franco Giovenzana and Annalisa Grossi},
     title = {O{\textquoteright}Grady tenfolds as moduli spaces of sheaves},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {12},
     year = {2024},
     doi = {10.1017/fms.2024.46},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.46/}
}
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Camilla Felisetti; Franco Giovenzana; Annalisa Grossi. O’Grady tenfolds as moduli spaces of sheaves. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.46

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