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arXiv · 2608.27441

Towards the Global Torelli Theorem

Daniil Serebrennikov
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Abstract

In this paper, we prove finiteness results for K-trivial varieties in all dimensions. In dimension 2, these results are corollaries of the Global Torelli Theorem for polarized K3 surfaces. In particular, we establish a sufficient condition when two fibers of a projective family of K-trivial varieties are isomorphic via the Hodge theory. As applications, we prove that if a projective family of K-trivial varieties has a dense subset of birationally equivalent fibers, then all fibers are isomorphic.

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Daniil Serebrennikov. 2026-08-27. Towards the Global Torelli Theorem. https://arxiv.org/abs/2608.27441

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