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2019 Positivity functions for curves on algebraic varieties
Brian Lehmann, Jian Xiao
Algebra Number Theory 13(6): 1243-1279 (2019). DOI: 10.2140/ant.2019.13.1243

Abstract

This is the second part of our work on Zariski decomposition structures, where we compare two different volume type functions for curve classes. The first function is the polar transform of the volume for divisor classes. The second function captures the asymptotic geometry of curves analogously to the volume function for divisors. We prove that the two functions coincide, generalizing Zariski’s classical result for surfaces to all varieties. Our result confirms the log concavity conjecture of the first named author for weighted mobility of curve classes in an unexpected way, via Legendre–Fenchel type transforms. During the course of the proof, we obtain a refined structure theorem for the movable cone of curves.

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Brian Lehmann. Jian Xiao. "Positivity functions for curves on algebraic varieties." Algebra Number Theory 13 (6) 1243 - 1279, 2019. https://doi.org/10.2140/ant.2019.13.1243

Information

Received: 2 March 2018; Revised: 20 February 2019; Accepted: 8 April 2019; Published: 2019
First available in Project Euclid: 21 August 2019

zbMATH: 07103973
MathSciNet: MR3994564
Digital Object Identifier: 10.2140/ant.2019.13.1243

Subjects:
Primary: 14C25
Secondary: 14C20 , 32J25

Keywords: algebraic varieties , mobility of cycles , positivity of curves , volume-type function , Zariski decomposition

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 6 • 2019
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