The cotangent space at a monomial ideal of the Hilbert scheme of points of an affine space
| dc.creator | Huibregtse, Mark E. | |
| dc.date | 2005-06-28 | |
| dc.date.accessioned | 2026-07-07T05:21:12Z | |
| dc.date.available | 2026-07-07T05:21:12Z | |
| dc.description | Let k be an algebraically closed field. We study the cotangent space of a point t corresponding to a monomial ideal I of k[x_1, ..., x_r] in the Hilbert scheme of n points of affine r-space (so the k-dimension of k[x_1, ..., x_r]/I = colength of I = n). Since t lies in the closure of the locus corresponding to subschemes supported at n distinct points of A^r_k, one knows that the k-dimension of the cotangent space is always >= r*n, and that t is nonsingular if and only if the dimension equals r*n. We construct an explicit linearly independent set S of cotangent vectors of size r*n, and then explore conditions on I under which S either is or is not a basis of the cotangent space. In particular, we give a condition on I sufficient for S to be a basis (equivalently, for t to be nonsingular) that holds for every monomial ideal in the case of r = 2 variables, and that characterizes such ideals when r = 3. We also give an easily-checked condition on I sufficient for S not to be a basis. | |
| dc.description | 51 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/math/0506575 | |
| dc.identifier | http://arxiv.org/abs/math/0506575 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75605 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 14C05 | |
| dc.title | The cotangent space at a monomial ideal of the Hilbert scheme of points of an affine space | |
| dc.type | text |