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Lagrangian fibrations of hyperk\"ahler fourfolds

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arxiv 1902.10440 v2 pith:VTZVYS3O submitted 2019-02-27 math.AG

classification math.AG
keywords lagrangianahlerbasefibrationfibrationsfourfoldfourfoldshyperk
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abstract

The base surface $B$ of a Lagrangian fibration $X\twoheadrightarrow B$ of a projective, irreducible symplectic fourfold $X$ is shown to be isomorphic to ${\mathbb P}^2$.

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  1. Numerical invariants of hyper-K\"ahler manifolds

    math.AG 2025-06 conditional novelty 6.0 of 10

    In dimension six, an isotropic class with extremal intersection numbers forces the Beauville form to be even and the Riemann-Roch polynomial to be one of a short list of explicit polynomials.

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