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This is a Quantitative Study study.

October 1, 2025Open Access

Geometry of regular semisimple Lusztig varieties

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Authors

PBPatrick BrosnanUniversity of Surrey JHJaehyun HongKorea Institute for Advanced Study DLDonggun LeeUniversity of Illinois Urbana-Champaign

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Implication

This analysis explores the geometry of lusztig varieties and regular semisimple Hessenberg varieties, indicating significant cohomological properties.

Key Points

Lusztig varieties exhibit normality and rational singularities, offering a structured framework for further exploration.
The cohomology of ample line bundles on these varieties vanishes, particularly highlighting its significance in positive characteristic.
A flat degeneration of regular semisimple lusztig varieties to Hessenberg varieties shows rich geometric relationships in algebraic geometry.
Key conjectures regarding homeomorphism types in type A are confirmed, indicating broader implications for various Lie types.

Cite This Study

Brosnan et al. (2025) studied this question.

synapsesocial.com/papers/68dd91cbfe798ba2fc4986c6 https://doi.org/10.48550/arxiv.2504.15868

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Implication

This analysis explores the geometry of lusztig varieties and regular semisimple Hessenberg varieties, indicating significant cohomological properties.

Geometry of regular semisimple Lusztig varieties

Discussion

Member takes

Implication

Key Points

Cite This Study

Geometry of regular semisimple Lusztig varieties

Discussion

Member takes

Implication

Key Points

Cite This Study

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