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Professor Chern recruited geometers, physicists and combinatorists to work at Nankai Institute of Mathematics (now Chern Institute of Mathematics).
We obtain a formula for the generating series of (the push-forward under the Hilbert-Chow morphism of) the Hirzebruch homology characteristic classes of the Hilbert schemes of points for a smooth quas...
Abstract: We provide an overview of the Macaulay2 package VersalDeformations, which algorithmically computes versal deformations of isolated singularities, as well as local (multi)graded Hilbert schem...
Abstract: Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the...
We show that a natural isomorphism between the rational cohomology groups of the two zero-dimensional Hilbert schemes of n-points of two surfaces, the affine plane minus the axes and the cotangent bun...
In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of $(1,k)$-quasi-homogeneous Hilbert schemes of points on th...
We seek to characterize homology classes of Lagrangian projective spaces embedded in irreducible holomorphic-symplectic manifolds, up to the action of the monodromy group. This paper addresses the ca...
Given a finite subgroup 􀀀  SL2(C) we define an additive 2-category H􀀀 whose Grothendieck group is isomorphic to an integral form h􀀀 of the Heisenberg algebra. We construct...
Let C be a locally planar curve. Its versal deformation admits a stratification by the genera of the fibres. The strata are singular; we show that their multiplicities at the central point are determ...
We prove the standard conjectures for complex projective varieties that are deformations of the Hilbert scheme of points on a K3 surface. The proof involves Verbitsky’s theory of hyperholomorphic shea...
We compute certain 1-point genus-0 Gromov-Witten invariants of the Hilbert scheme of points on a simply-connected smooth projective surface.

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