Local effectivity in projective spaces

2018/02/23 by Marcin Dumnicki, Dumnicki, Marcin, Tomasz Szemberg +3
Mathematics · #13A15 #13F20 #14C20 #14J26 #14N20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1802.08699

openalex publication_date 2018/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we introduce a Waldschmidt decomposition of divisors which might be viewed as a generalization of Zariski decomposition based on the effectivity rather than the nefness of divisors. As an immediate application we prove a recursive formula providing new effective lower bounds on Waldschmidt constants of very general points in projective spaces. We use these bounds in order to verify Demailly's conjecture in a number of new cases.

Citations

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