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arXiv · 1902.04668

A reconstruction theorem for varieties

Max Lieblich·Martin Olsson
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Abstract

We show that varieties of dimension at least 2 over infinite fields are determined as abstract schemes by their Zariski topological spaces together with the rational equivalence relation on the set of effective divisors. This gives a universal Torelli theorem in the sense of Bogomolov and Tschinkel. The proof relies heavily on a rational version of the classical Fundamental Theorem of Projective Geometry.

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Max Lieblich, Martin Olsson. 2019-02-12. A reconstruction theorem for varieties. https://arxiv.org/abs/1902.04668

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