Tautological integrals on Hilbert scheme of points I

2023/03/26 by Gergely Bérczi, Bérczi, Gergely
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2303.14807

openalex publication_date 2023/03/26 · openalex created_date 2023/03/31 · openalex updated_date 2026/08/03

Abstract

We develop a new method to study intersection theory of the main component of the Hilbert scheme of points on complex manifolds. The main result is an iterated residue formula for tautological integrals. We formulate a Chern-Segre-type positivity conjecture for these integrals, and we introduce higher dimensional Segre and Chern integrals.

Related

• Tautological integrals on Hilbert scheme of points II: Geometric subsets
• Tautological Integrals on Hilbert Schemes of Points on Curves
• Higher rank Segre integrals over the Hilbert scheme of points
• Segre classes and Hilbert schemes of points
• Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)