Nested Hilbert schemes and the nested q,t-Catalan series
| dc.creator | Can, Mahir Bilen | |
| dc.date | 2007-11-05 | |
| dc.date.accessioned | 2026-07-07T08:40:56Z | |
| dc.date.available | 2026-07-07T08:40:56Z | |
| dc.description | In this paper we study the tangent spaces of the smooth nested Hilbert scheme $ Hil{n,n-1}$ of points in the plane, and give a general formula for computing the Euler characteristic of a $\TT^2$-equivariant locally free sheaf on $\Hil{n,n-1}$. 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 \textsl{the nested $q,t$-Cat alan series}, for it has many conjectural properties similar to that of the $q,t $-Catalan series. | |
| dc.description | 28 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/0711.0763 | |
| dc.identifier | http://arxiv.org/abs/0711.0763 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141526 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 14M15; 05E15 | |
| dc.title | Nested Hilbert schemes and the nested q,t-Catalan series | |
| dc.type | text |