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Journal Article

Wall divisors and algebraically coisotropic subvarieties of irreducible holomorphic symplectic manifolds

MPS-Authors
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Lelli-Chiesa,  Margherita
Max Planck Institute for Mathematics, Max Planck Society;

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Mongardi,  Giovanni
Max Planck Institute for Mathematics, Max Planck Society;

External Ressource

https://doi.org/10.1090/tran/7340
(Publisher version)

Fulltext (public)

arXiv:1507.06891.pdf
(Preprint), 482KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Knutsen, A. L., Lelli-Chiesa, M., & Mongardi, G. (2019). Wall divisors and algebraically coisotropic subvarieties of irreducible holomorphic symplectic manifolds. Transactions of the American Mathematical Society, 371(2), 1403-1438. doi:10.1090/tran/7340.


Cite as: http://hdl.handle.net/21.11116/0000-0004-F1C9-9
Abstract
Rational curves on Hilbert schemes of points on $K3$ surfaces and generalised Kummer manifolds are constructed by using Brill-Noether theory on nodal curves on the underlying surface. It turns out that all wall divisors can be obtained, up to isometry, as dual divisors to such rational curves. The locus covered by the rational curves is then described, thus exhibiting algebraically coisotropic subvarieties. This provides strong evidence for a conjecture by Voisin concerning the Chow ring of irreducible holomorphic symplectic manifolds. Some general results concerning the birational geometry of irreducible holomorphic symplectic manifolds are also proved, such as a non-projective contractibility criterion for wall divisors.