Nested Hilbert Schemes and the Nested Q,t-catalan Series
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چکیده
In this paper we study the tangent spaces of the smooth nested Hilbert scheme Hilb n,n−1 (A 2) of points in the plane, and give a general formula for computing the Euler characteristic of a T 2-equivariant locally free sheaf on Hilb n,n−1 (A 2). Applying our result to a particular sheaf, we conjecture that the result is a polynomial in the variables q and t with non-negative integer coefficients. We call this conjecturally positive polynomial as the nested q, t-Catalan series, for it has many conjectural properties similar to that of the q, t-Catalan series.
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Nested Hilbert Schemes and the nested q, t-Catalan series
In this paper we study the tangent spaces of the smooth nested Hilbert scheme Hilbn,n−1(A2) of points in the plane, and give a general formula for computing the Euler characteristic of a T-equivariant locally free sheaf on Hilbn,n−1(A2). Applying our result to a particular sheaf, we conjecture that the result is a polynomial in the variables q and t with non-negative integer coefficients. We ca...
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