Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part I

F. Reese Harvey; H. Blaine Lawson

doi:10.1093/acprof:oso/9780199534920.003.0013

Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part I

F. Reese Harvey
, H. Blaine Lawson

Mathematics

Rice University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

In 2000, H. Alexander and J. Wermer published the following result: Let Γ be a compact-oriented smooth submanifold of dimension 2p - 1 in n. Then Γ bounds a positive holomorphic p-chain in n if and only if the linking number Link(Γ, Z) ≥ 0 for all canonically oriented algebraic subvarieties Z of codimension p in n - Γ. This chapter formulates and proves an analogue of the Alexander-Wermer theorem for oriented (not necessarily connected) curves in a projective manifold.

Original language	English
Title of host publication	The Many Facets of Geometry
Subtitle of host publication	A Tribute to Nigel Hitchin
Publisher	Oxford University Press
ISBN (Electronic)	9780191716010
ISBN (Print)	9780199534920
DOIs	https://doi.org/10.1093/acprof:oso/9780199534920.003.0013
State	Published - Sep 1 2010

Keywords

Alexander-Wermer theorem
H. Alexander and J. Wermer
Oriented curves
Projective manifold

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10.1093/acprof:oso/9780199534920.003.0013

Cite this

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N2 - In 2000, H. Alexander and J. Wermer published the following result: Let Γ be a compact-oriented smooth submanifold of dimension 2p - 1 in n. Then Γ bounds a positive holomorphic p-chain in n if and only if the linking number Link(Γ, Z) ≥ 0 for all canonically oriented algebraic subvarieties Z of codimension p in n - Γ. This chapter formulates and proves an analogue of the Alexander-Wermer theorem for oriented (not necessarily connected) curves in a projective manifold.

AB - In 2000, H. Alexander and J. Wermer published the following result: Let Γ be a compact-oriented smooth submanifold of dimension 2p - 1 in n. Then Γ bounds a positive holomorphic p-chain in n if and only if the linking number Link(Γ, Z) ≥ 0 for all canonically oriented algebraic subvarieties Z of codimension p in n - Γ. This chapter formulates and proves an analogue of the Alexander-Wermer theorem for oriented (not necessarily connected) curves in a projective manifold.

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KW - H. Alexander and J. Wermer

KW - Oriented curves

KW - Projective manifold

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SN - 9780199534920

BT - The Many Facets of Geometry

PB - Oxford University Press

ER -

Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part I

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