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arXiv · 2109.03987

The dual Lagrangian fibration of known hyper-K\"ahler manifolds

Yoon-Joo Kim
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Abstract

Given a Lagrangian fibration $\pi : X \to \mathbb{P}^n$ of a compact hyper-K\"ahler manifold of $\text{K3}^{[n]}$, $\text{Kum}_n$, $\text{OG10}$ or $\text{OG6}$-type, we construct a natural compactification of its dual torus fibration. Specifically, this compactification is given by a quotient of $X$ by certain automorphisms acting trivially on the second cohomology and respecting the Lagrangian fibration. It is a compact hyper-K\"ahler orbifold with identical period mapping behavior as $X$.

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Yoon-Joo Kim. 2021-09-09. The dual Lagrangian fibration of known hyper-K\"ahler manifolds. https://arxiv.org/abs/2109.03987

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