Singular support and Characteristic cycle of a rank one sheaf in codimension two

2022/06/07 by Yuri Yatagawa, Yatagawa, Yuri
Computer Science · Engineering · Mathematics · #11S15 (Primary) #14F20 (Secondary) #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2206.02989

openalex publication_date 2022/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the singular support and the characteristic cycle of a rank 1 sheaf on a smooth variety in codimension 2 using ramification theory, when the ramification of the sheaf is clean. We develop a general theory, called the partially logarithmic ramification theory, and define an algebraic cycle on a logarithmic cotangent bundle with partial logarithmic poles along the boundary. We prove that the inverse image of the support of the cycle and the pull-back of the cycle to the cotangent bundle are equal to the singular support and the characteristic cycle, respectively, outside a closed subset of the variety of codimension greater than 2 under a mild assumption.

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• Characteristic cycles of constructible sheaves and microlocalization
• Comparison of the two notions of characteristic cycles
• Relative singular support and the semi-continuity of characteristic cycles for étale sheaves
• Notes on the characteristic cycle of a constructible sheaf