The Demailly systems with the vortex ansatz

Arindam Mandal

doi:10.1016/j.bulsci.2023.103307

The Demailly systems with the vortex ansatz

Arindam Mandal

Mathematics

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

3 Scopus citations

Abstract

For an arbitrary-rank vector bundle over a projective manifold, J.-P. Demailly proposed several systems of equations of Hermitian-Yang-Mills type for the curvature tensor to settle a conjecture of Griffiths on the equivalence of Hartshorne ampleness and Griffiths positivity. In this article, we have studied two proposed systems and proved that these equations have smooth solutions for the Vortex bundle using the continuity method.

Original language	English
Article number	103307
Journal	Bulletin des Sciences Mathematiques
Volume	187
DOIs	https://doi.org/10.1016/j.bulsci.2023.103307
State	Published - Oct 2023

Keywords

Ample vector bundle
Curvature tensor
Dual Nakano positivity
Elliptic operator
Griffiths positivity
Nakano positivity

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10.1016/j.bulsci.2023.103307

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title = "The Demailly systems with the vortex ansatz",

abstract = "For an arbitrary-rank vector bundle over a projective manifold, J.-P. Demailly proposed several systems of equations of Hermitian-Yang-Mills type for the curvature tensor to settle a conjecture of Griffiths on the equivalence of Hartshorne ampleness and Griffiths positivity. In this article, we have studied two proposed systems and proved that these equations have smooth solutions for the Vortex bundle using the continuity method.",

keywords = "Ample vector bundle, Curvature tensor, Dual Nakano positivity, Elliptic operator, Griffiths positivity, Nakano positivity",

author = "Arindam Mandal",

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year = "2023",

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AB - For an arbitrary-rank vector bundle over a projective manifold, J.-P. Demailly proposed several systems of equations of Hermitian-Yang-Mills type for the curvature tensor to settle a conjecture of Griffiths on the equivalence of Hartshorne ampleness and Griffiths positivity. In this article, we have studied two proposed systems and proved that these equations have smooth solutions for the Vortex bundle using the continuity method.

KW - Ample vector bundle

KW - Curvature tensor

KW - Dual Nakano positivity

KW - Elliptic operator

KW - Griffiths positivity

KW - Nakano positivity

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DO - 10.1016/j.bulsci.2023.103307

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SN - 0007-4497

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JO - Bulletin des Sciences Mathematiques

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The Demailly systems with the vortex ansatz

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Keywords

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