Abstract
We prove that there are at most two possibilities for the base of a Lagrangian fibration from a complex projective irreducible symplectic fourfold.
Acknowledgements
The author is very grateful to his advisor S. Druel for suggesting him this question and for his useful comments. He is thankful to M. Brion, D. Huybrechts and C. Lehn for helpful discussions. He would like to thank A. Höring for suggesting a simple proof for Proposition 4.11. He also wants to thank the referee for suggestions on the exposition.
References
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