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<p>In this article, we study the asymptotic behavior of harmonic 2-forms on <i>K</i>3 surfaces with Ricci-flat Kähler metrics, where metrics converge to the quotient of a flat 4-dimensional torus by a finite group action. We can show that the space of anti-self-dual harmonic 2-forms decomposes into two subspaces: one converges to the flat 2-forms on the quotient of the torus, while the other converges to the first Chern forms of anti-self-dual connections on ALE spaces.</p>

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The Harmonic 2-forms on K3 Surfaces Converging to a Flat 4-Dimensional Orbifold

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  • 发表日期：

    2026年5月22日

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  • Kota Hattori

摘要

In this article, we study the asymptotic behavior of harmonic 2-forms on K3 surfaces with Ricci-flat Kähler metrics, where metrics converge to the quotient of a flat 4-dimensional torus by a finite group action. We can show that the space of anti-self-dual harmonic 2-forms decomposes into two subspaces: one converges to the flat 2-forms on the quotient of the torus, while the other converges to the first Chern forms of anti-self-dual connections on ALE spaces.