What determines a variety?

2020/02/27 by Janós Kollár, Kollár, János
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2002.12424

openalex publication_date 2020/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, over a field of characteristic 0, a normal, projective variety of dimension at least 4 is uniquely determined by its underlying topological space. The proof builds on previous work of Lieblich and Olsson. Version 2: many small changes and new references.

Citations

• Specialization of Néron-Severi groups in positive characteristic
• Abelian Varieties and Finitely Generated Galois Groups

Cited by

• A reconstruction theorem for varieties

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• Reconstructing a variety from its topology (after Kollár, building on earlier work of Lieblich and Olsson)
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