The affine stratification number and the moduli space of curves
| dc.creator | Roth, Mike | |
| dc.creator | Vakil, Ravi | |
| dc.date | 2004-06-19 | |
| dc.date.accessioned | 2026-07-07T05:09:23Z | |
| dc.date.available | 2026-07-07T05:09:23Z | |
| dc.description | We define the affine stratification number asn X of a scheme X. For X equidimensional, it is the minimal number k such that there is a stratification of X by locally closed affine subschemes of codimension at most k. We show that the affine stratification number is well-behaved, and bounds many aspects of the topological complexity of the scheme, such as vanishing of cohomology groups of quasicoherent, constructible, and l-adic sheaves. We explain how to bound asn X in practice. We give a series of conjectures (the first by E. Looijenga) bounding the affine stratification number of various moduli spaces of pointed curves. For example, the philosophy of [GV, Theorem *] yields: the moduli space of genus g, n-pointed complex curves of compact type (resp. with "rational tails") should have the homotopy type of a finite complex of dimension at most 5g-6+2n (resp. 4g-5+2n). This investigation is based on work and questions of Looijenga. One relevant example turns out to be a proper integral variety with no embeddings in a smooth algebraic space. This one-paragraph construction appears to be simpler and more elementary than the earlier examples, due to Horrocks and Nori. | |
| dc.description | 17 pages, to appear in Proceedings of "Workshop on algebraic structures and moduli spaces", July 14-20, 2003, Centre de Recherches Mathematiques, Universite de Montreal | |
| dc.identifier | https://arxiv.org/abs/math/0406384 | |
| dc.identifier | http://arxiv.org/abs/math/0406384 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71611 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Primary 14A15, Secondary 14H10 | |
| dc.title | The affine stratification number and the moduli space of curves | |
| dc.type | text |