Constructing projective varieties in weighted flag varieties II

Muhammad Imran Qureshi

doi:10.1017/S0305004114000620

Constructing projective varieties in weighted flag varieties II

Muhammad Imran Qureshi

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

11 Scopus citations

Abstract

We give the construction of weighted Lagrangian Grassmannians wLGr(3,6) and weighted partial A ₃ flag variety wFL_1,3 coming from the symplectic Lie group Sp(6, ℂ) and the general linear group GL(4, ℂ) respectively. We give general formulas for their Hilbert series in terms of Lie theoretic data. We use them as key varieties (Format) to construct some families of polarized 3-folds in codimension 7 and 9. Finally, we list all the distinct weighted flag varieties in codimension (4 ≤ c ≤ 10.

Original language	English
Pages (from-to)	193-209
Number of pages	17
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	158
Issue number	2
DOIs	https://doi.org/10.1017/S0305004114000620
State	Published - 11 Mar 2015
Externally published	Yes

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Publisher Copyright:
Copyright © Cambridge Philosophical Society 2015

ASJC Scopus subject areas

General Mathematics

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10.1017/S0305004114000620

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abstract = "We give the construction of weighted Lagrangian Grassmannians wLGr(3,6) and weighted partial A 3 flag variety wFL1,3 coming from the symplectic Lie group Sp(6, ℂ) and the general linear group GL(4, ℂ) respectively. We give general formulas for their Hilbert series in terms of Lie theoretic data. We use them as key varieties (Format) to construct some families of polarized 3-folds in codimension 7 and 9. Finally, we list all the distinct weighted flag varieties in codimension (4 ≤ c ≤ 10.",

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AB - We give the construction of weighted Lagrangian Grassmannians wLGr(3,6) and weighted partial A 3 flag variety wFL1,3 coming from the symplectic Lie group Sp(6, ℂ) and the general linear group GL(4, ℂ) respectively. We give general formulas for their Hilbert series in terms of Lie theoretic data. We use them as key varieties (Format) to construct some families of polarized 3-folds in codimension 7 and 9. Finally, we list all the distinct weighted flag varieties in codimension (4 ≤ c ≤ 10.

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Constructing projective varieties in weighted flag varieties II

Abstract

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