Incidence strata of affine varieties with complex multiplicities

2019/03/12 by Hunter Spink, Spink, Hunter, Dennis Tseng +1
Computer Science · Mathematics · #14B05 #14D20 #18D10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1903.05011

openalex publication_date 2019/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To each affine variety X and m₁,…,m_k∈ ℂ such that no subset of the m_i add to zero, we construct a variety which for m₁,…,m_k ∈ ℕ specializes to the closed (m₁,…,m_k)-incidence stratum of Sym^m₁+…+m_kX. These fit into a finite-type family, which is functorial in X, and which is topologically a family of ℂ-weighted configuration spaces. We verify our construction agrees with an analogous construction in the Deligne category Rep(S_d) for d ∈ ℂ. We next classify the singularity locus and branching behaviour of colored incidence strata for arbitrary smooth curves. As an application, we negatively answer a question of Farb and Wolfson concerning the existence of an isomorphism between two natural moduli spaces.

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