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

2023/04/19 by Hongyi Liu, Liu, Hongyi · 2 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2304.09501

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 hyperkähler 4-manifolds developped by Sun-Zhang, and does not rely on the solution to the Calabi conjecture.

Cited by

• Compactification of metric moduli space of K3 surfaces
• On multiscale aspects of Kähler-Einstein metrics and algebraic geometry

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