Stringy motives of symmetric products

2006/08/13 by Sergey Mozgovoy, Mozgovoy, Sergey
Mathematics · #14Q15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.math/0608323

openalex publication_date 2006/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a complex smooth algebraic variety X, we compute the generating function of the stringy motives of its symmetric powers as a function of motive of X. In dimension two we recover the Goettsche formulas for Hilbert schemes. We use the formalism of lambda-rings to get a particularly compact formula, which is convenient for explicit computations.

Citations

• Mixed Hodge structures of configuration spaces

Related

• The motive of the Hilbert scheme of points in all dimensions
• On the motive of the Quot scheme of finite quotients of a locally free\n sheaf
• Abelian motives and Shimura varieties in nonzero characteristic
• Motives meet SymPy: studying λ-ring expressions in Python
• On the behavior of stringy motives under Galois quasi-étale covers