Singularities of Fano varieties of lines on singular cubic fourfolds

Ryo Yamagishi

doi:10.2969/jmsj/82688268

July 6, 2021Journal of the Mathematical Society of Japan

Singularities of Fano varieties of lines on singular cubic fourfolds

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Key Points

The research aims to establish the relationship between the singularities of Fano varieties and those of Hilbert schemes on surfaces with ADE singularities.
Analysis of simple singularities in cubic fourfolds.
Comparison of Fano varieties of lines with Hilbert schemes of points.
Theoretical proofs regarding analytic types.
Demonstrated that the Fano variety of lines on cubic fourfolds shares analytic singularity types with the Hilbert scheme of two points.
Identified that both structures are categorized by ADE singularities.

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Implication

Assesses the singularity type of Fano varieties in cubic fourfolds, suggesting important mathematical connections.

Abstract

Let X be a cubic fourfold that has only simple singularities and does not contain a plane. We prove that the Fano variety of lines on X has the same analytic type of singularity as the Hilbert scheme of two points on a surface with only ADE-singularities.

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Ryo Yamagishi (2021) studied this question.

synapsesocial.com/papers/6a5dfb59a5f26c43a2d89636 https://doi.org/10.2969/jmsj/82688268

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Singularities of Fano varieties of lines on singular cubic fourfolds

Key Points

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Implication

Abstract

Discussion

Cite This Study

Singularities of Fano varieties of lines on singular cubic fourfolds

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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