Characterizing volume via cone duality

Jian Xiao

doi:10.1007/s00208-016-1501-3

Characterizing volume via cone duality

Jian Xiao^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

For divisors over smooth projective varieties, we show that the volume can be characterized by the duality between the pseudo-effective cone of divisors and the movable cone of curves. Inspired by this result, we define and study a natural intersection-theoretic volume functional for 1-cycles over compact Kähler manifolds. In particular, for numerical equivalence classes of curves over projective varieties, it is closely related to the mobility functional studied by Lehmann.

Original language	English (US)
Pages (from-to)	1527-1555
Number of pages	29
Journal	Mathematische Annalen
Volume	369
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-016-1501-3
State	Published - Dec 1 2017

Keywords

32J18
32J25

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00208-016-1501-3

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title = "Characterizing volume via cone duality",

abstract = "For divisors over smooth projective varieties, we show that the volume can be characterized by the duality between the pseudo-effective cone of divisors and the movable cone of curves. Inspired by this result, we define and study a natural intersection-theoretic volume functional for 1-cycles over compact K{\"a}hler manifolds. In particular, for numerical equivalence classes of curves over projective varieties, it is closely related to the mobility functional studied by Lehmann.",

keywords = "32J18, 32J25",

author = "Jian Xiao",

note = "Funding Information: Acknowledgements I would like to thank my supervisor Jean-Pierre Demailly for suggesting this topic and helpful suggestions, and thank Mattias Jonsson and Brian Lehmann for many useful discussions, and thank the referee for several helpful comments. This work is supported by China Scholarship Council. Publisher Copyright: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",

year = "2017",

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doi = "10.1007/s00208-016-1501-3",

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T1 - Characterizing volume via cone duality

AU - Xiao, Jian

N1 - Funding Information: Acknowledgements I would like to thank my supervisor Jean-Pierre Demailly for suggesting this topic and helpful suggestions, and thank Mattias Jonsson and Brian Lehmann for many useful discussions, and thank the referee for several helpful comments. This work is supported by China Scholarship Council. Publisher Copyright: © 2016, Springer-Verlag Berlin Heidelberg.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - For divisors over smooth projective varieties, we show that the volume can be characterized by the duality between the pseudo-effective cone of divisors and the movable cone of curves. Inspired by this result, we define and study a natural intersection-theoretic volume functional for 1-cycles over compact Kähler manifolds. In particular, for numerical equivalence classes of curves over projective varieties, it is closely related to the mobility functional studied by Lehmann.

AB - For divisors over smooth projective varieties, we show that the volume can be characterized by the duality between the pseudo-effective cone of divisors and the movable cone of curves. Inspired by this result, we define and study a natural intersection-theoretic volume functional for 1-cycles over compact Kähler manifolds. In particular, for numerical equivalence classes of curves over projective varieties, it is closely related to the mobility functional studied by Lehmann.

KW - 32J18

KW - 32J25

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DO - 10.1007/s00208-016-1501-3

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SN - 0025-5831

VL - 369

SP - 1527

EP - 1555

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

Characterizing volume via cone duality

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Keywords

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