The harmonic $2$-forms on $K3$ surfaces converging to a flat $4$-dimensional orbifold

Kota Hattori

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arXiv · 2512.14125

The harmonic $2$-forms on $K3$ surfaces converging to a flat $4$-dimensional orbifold

Kota Hattori

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Abstract

In this article, we study the asymptotic behavior of harmonic $2$-forms on $K3$ surfaces with Ricci-flat K\"ahler metrics, where metrics converge to the quotient of a flat $4$-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.

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BibTeX RIS

Kota Hattori. 2025-12-16. The harmonic $2$-forms on $K3$ surfaces converging to a flat $4$-dimensional orbifold. https://arxiv.org/abs/2512.14125

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