Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/9803091

Chern Classes of Tautological Sheaves on Hilbert Schemes

Manfred Lehn
View original source ↗Read source document ↗Export metadata ↓

Abstract

We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces within the framework of Nakajima's oscillator algebra. This leads to an identification of the cohomology ring of Hilbert schemes of the affine plane with a ring of differential operators on a Fock space. We end with the computation of the top Segre classes of tautological bundles associated to line bundles on Hilb^n up to n=7, and give a conjecture for the generating series.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Manfred Lehn. 1998-03-20. Chern Classes of Tautological Sheaves on Hilbert Schemes. https://doi.org/10.1007/s002220050307

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Geometric Detection and Finiteness of Log Crystalline Local Systems

We prove a geometric detection theorem for log crystalline local systems in the smooth proper setting with a normal crossings boundary. The associated special-fiber log $F$-isocrystal detects geometric absolute irreducibility and, modulo constant rank-one twists, determines the pullback to the geometric generic fiber. The main ingredient is a determinant argument combining a finite-order rank-one reduction, logarithmic period comparison, and the Plücker embedding. As an application, using Abe--Esnault's finiteness theorem and finiteness of stable lattices, we prove finiteness, up to geometrically constant rank-one twists, of geometrically absolutely irreducible log crystalline local systems of fixed rank. Coefficients may lie in any fixed finite extension of $\mathbb Q_p$, and no bound on the Hodge--Tate weights is imposed.

math.AG↗
arXiv2026

Betti Numbers of Odd Biisotropic Symplectic Grassmannians

We compute the singular cohomology groups of odd biisotropic symplectic Grassmannians $\operatorname{S_2Gr}(k, 2n+1)$ by presenting an explicit dimension-preserving combinatorial bijection between the Bialynicki-Birula cells in $\operatorname{S_2Gr}(k, 2n+1)$ and the Schubert cells in $\operatorname{Gr}(k, 2n+2-k)$.

math.AG↗
arXiv2026

Motivic $C_p$-power operations in $\mathrm{MGL}$

In this paper, we give a new proof of the Hopkins-Morel-Hoyois theorem for fields $k$ of characteristic unequal to $p$ containing all primitive $p$-power roots of unity for a fixed prime $p$. This new proof follows Quillen's proof for the structure of the homotopy groups of $\mathrm{MU}$ which utilizes topological power operations. To this end we define a motivic analog of the Steenrod power operations, using the theory of normed motivic spectra as developed by Bachmann--Hoyois and their application for the definition of motivic colimits as developed by Bachmann-Elmanto-Heller.

math.AG↗