On Duistermaat-Heckman measure for filtered linear series

2019/04/30 by Nathan Grieve, Grieve, Nathan · 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.1904.13184

openalex publication_date 2019/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit work of S. Boucksom, C. Favre, and M. Jonsson (J. Algebraic Geom. 18 (2009), no. 2, 279--308); Boucksom and H. Chen (Compos. Math. 147 (2011), no. 4, 1205--1229); and S. Boucksom, A. Küronya, C. Maclean, and T. Szemberg (Math. Ann. 361 (2015), no.~3--4, 811--834). The key point is to associate a Duistermaat-Heckman measure to a filtered big linear series on a given projective variety. The expectation of the measure admits a description via the theory of Newton-Okounkov bodies. Such considerations have origins in symplectic geometry. They have applications for K-stability and Diophantine arithmetic geometry of projective varieties.

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