Abstract
We survey some results about rational curves on hyperkähler manifolds, explaining how to prove a certain deformation-invariance statement for loci covered by rational curves with negative Beauville–Bogomolov square.
The results presented at the INDAM workshop and in this survey have been obtained jointly with M. Verbitsky.
Partially supported by Brazilian-French network in Mathematics, partially supported by the Russian Academic Excellence Project ‘5-100’.
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Notes
- 1.
On an arbitrary deformation, an MBM class would be, up to a multiple, represented by a possibly reducible rational curve, but the converse is in general false.
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Amerik, E. (2020). Negative Rational Curves and Their Deformations on Hyperkähler Manifolds. In: Colombo, E., Fantechi, B., Frediani, P., Iacono, D., Pardini, R. (eds) Birational Geometry and Moduli Spaces. Springer INdAM Series, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-030-37114-2_1
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