On Okounkov's conjecture connecting Hilbert schemes of points and multiple q-zeta values

2015/10/03 by Zhenbo Qin, Fei Yu, Qin, Zhenbo +1 · 2 citations
Mathematics · #17B69 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Primary 14C05 #Representation Theory (math.RT) #Secondary 11B65

paper · pdf · doi:10.48550/arxiv.1510.00837

openalex publication_date 2015/10/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We compute the generating series for the intersection pairings between the total Chern classes of the tangent bundles of the Hilbert schemes of points on a smooth projective surface and the Chern characters of tautological bundles over these Hilbert schemes. Modulo the lower weight term, we verify Okounkov's conjecture [Oko] connecting these Hilbert schemes and multiple q-zeta values. In addition, this conjecture is completely proved when the surface is abelian. We also determine some universal constants in the sense of Boissi' ere and Nieper-Wisskirchen [Boi, BN] regarding the total Chern classes of the tangent bundles of these Hilbert schemes. The main approach of this paper is to use the set-up of Carlsson and Okounkov outlined in [Car, CO] and the structure of the Chern character operators proved in [LQW2].

Cited by

• Equivariant Chern character operators and Okounkov's conjecture
• Multiple q-zeta values and traces

Related

• Hilbert schemes of points on surfaces and multiple q-zeta values
• Toward Qin's Conjecture on Hilbert schemes of points and quasi-modular forms
• Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane
• Generating series in the cohomology of Hilbert schemes of points on surfaces
• Tautological Integrals on Hilbert Schemes of Points on Curves