Invariance of plurigenera fails in positive and mixed characteristic

2020/11/20 by Iacopo Brivio, Brivio, Iacopo · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2011.10226

openalex publication_date 2020/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct smooth families of elliptic surface pairs with terminal singularities over a DVR of positive or mixed characteristic (X,B)→ SpecR, such that P_m(X_k,B_k)>P_m(X_K,B_K) for all sufficiently divisible m>0. In particular, this shows that invariance of all sufficiently divisible plurigenera does not follow from the MMP and Abundance Conjectures.

Cited by

• Non-extendable MMPs

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