2021/05/30 by David Villalobos-Paz, Villalobos-Paz, David
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2105.14630
openalex publication_date 2021/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that a smooth Moishezon space Y is non-projective if and only if it contains a rational curve such that -[C] ∈ NE(Y). More generally, this holds if Y has ℚ-factorial, log terminal singularities. We derive this as a consequence of our main technical result: that we can run the relative minimal model program when the base is a normal algebraic space Y of finite type over a field of characteristic 0. As a second application, we show that every log canonical pair (Y, Δ), where Y is an algebraic space of finite type over a field of characteristic 0 admits a dlt modification that is projective over Y.