A short proof of the surjectivity of the period map on K3 manifolds

Hongyi Liu

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arXiv · 2304.09501

A short proof of the surjectivity of the period map on K3 manifolds

Hongyi Liu

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Abstract

In this note, we give a simple proof of the Todorov's surjectivity result on the period map of K3 surfaces in a differential geometric setting. Our proof makes use of collasping geometry of hyperk\"{a}hler 4-manifolds developped by Sun-Zhang, and does not rely on the solution to the Calabi conjecture.

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Hongyi Liu. 2023-04-19. A short proof of the surjectivity of the period map on K3 manifolds. https://arxiv.org/abs/2304.09501

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