Polarized 3-folds in a codimension 10 weighted homogeneous F4 variety

Muhammad Imran Qureshi

doi:10.1016/j.geomphys.2017.05.011

Polarized 3-folds in a codimension 10 weighted homogeneous F₄ variety

Muhammad Imran Qureshi

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

4 Scopus citations

Abstract

We describe the construction of a codimension 10 weighted homogeneous variety wΣF₄(μ,u) corresponding to the exceptional Lie group F₄ by explicit computation of its graded ring structure. We give a formula for the Hilbert series of the generic weighted wΣF₄(μ,u) in terms of representation theoretic data of F₄. We also construct some families of polarized 3-folds in codimension 10 whose general member is a weighted complete intersection of some wΣF₄(μ,u).

Original language	English
Pages (from-to)	52-61
Number of pages	10
Journal	Journal of Geometry and Physics
Volume	120
DOIs	https://doi.org/10.1016/j.geomphys.2017.05.011
State	Published - Oct 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

Graded rings
Lie group F
Polarized 3-folds
Weighted homogeneous variety

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

Access to Document

10.1016/j.geomphys.2017.05.011

Cite this

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title = "Polarized 3-folds in a codimension 10 weighted homogeneous F4 variety",

abstract = "We describe the construction of a codimension 10 weighted homogeneous variety wΣF4(μ,u) corresponding to the exceptional Lie group F4 by explicit computation of its graded ring structure. We give a formula for the Hilbert series of the generic weighted wΣF4(μ,u) in terms of representation theoretic data of F4. We also construct some families of polarized 3-folds in codimension 10 whose general member is a weighted complete intersection of some wΣF4(μ,u).",

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N2 - We describe the construction of a codimension 10 weighted homogeneous variety wΣF4(μ,u) corresponding to the exceptional Lie group F4 by explicit computation of its graded ring structure. We give a formula for the Hilbert series of the generic weighted wΣF4(μ,u) in terms of representation theoretic data of F4. We also construct some families of polarized 3-folds in codimension 10 whose general member is a weighted complete intersection of some wΣF4(μ,u).

AB - We describe the construction of a codimension 10 weighted homogeneous variety wΣF4(μ,u) corresponding to the exceptional Lie group F4 by explicit computation of its graded ring structure. We give a formula for the Hilbert series of the generic weighted wΣF4(μ,u) in terms of representation theoretic data of F4. We also construct some families of polarized 3-folds in codimension 10 whose general member is a weighted complete intersection of some wΣF4(μ,u).

KW - Graded rings

KW - Lie group F

KW - Polarized 3-folds

KW - Weighted homogeneous variety

UR - https://www.scopus.com/pages/publications/85033409245

U2 - 10.1016/j.geomphys.2017.05.011

DO - 10.1016/j.geomphys.2017.05.011

M3 - Article

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SP - 52

EP - 61

JO - Journal of Geometry and Physics

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