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arXiv · 1604.05261

On the primitivity of birational transformations of irreducible symplectic manifolds

Federico Lo Bianco
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Abstract

Let $f\colon X\dashrightarrow X$ be a bimeromorphic transformation of a complex irreducible symplectic manifold $X$. Some important dynamical properties of $f$ are encoded by the induced linear automorphism $f^*$ of $H^2(X,\mathbb Z)$. Our main result is that a bimeromorphic transformation such that $f^*$ has at least one eigenvalue with modulus $>1$ doesn't admit any invariant fibration (in particular its generic orbit is Zariski-dense).

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Federico Lo Bianco. 2016-04-18. On the primitivity of birational transformations of irreducible symplectic manifolds. https://arxiv.org/abs/1604.05261

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