Trim resolutions, stringy and Mather classes, and IC characteristic cycles

2025/12/08 by Aluffi, Paolo
Mathematics · #14C17 #32S60 #57R20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2512.07967

openalex publication_date 2025/12/08 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

Abstract

We introduce trim resolutions of complex algebraic varieties, a strengthening of the notion of small resolution. We prove that the characteristic cycle of the intersection cohomology sheaf of a variety admitting a trim resolution is irreducible and that for such varieties the stringy and Chern-Mather classes coincide.

Citations

• Characteristic cycles of IH sheaves of simply laced minuscule Schubert varieties are irreducible
• The Decomposition Theorem and the topology of algebraic maps
• Stringy Chern classes of singular varieties
• The Chow motive of semismall resolutions
• On the reducibility of characteristic varieties
• Non-Archimedian integrals and stringy Euler numbers of log terminal\n pairs
• Characteristic Classes of Hypersurfaces and Characteristic Cycles
• On the singularities of the theta divisors on Jacobians

Related

• The resolution property holds away from codimension three
• Characteristic cycles of IH sheaves of simply laced minuscule Schubert varieties are irreducible
• A canonical lift of Chern-Mather classes
• Characteristic cycles of constructible sheaves and microlocalization
• Singularities and Enriched Cycles