A Remark on the Geometry of Elliptic Scrolls and Bielliptic Surfaces
| dc.creator | Ciliberto, C. | |
| dc.creator | Hulek, K. | |
| dc.date | 1997-03-07 | |
| dc.date.accessioned | 2026-07-07T09:07:12Z | |
| dc.date.available | 2026-07-07T09:07:12Z | |
| dc.description | The union of two quintic elliptic scrolls in P^4 intersecting transversally along an elliptic normal quintic curve is a singular surface Z which behaves numerically like a bielliptic surface. In the appendix to the paper [W. Decker et al.: Syzygies of abelian and bielliptic surfaces in P^4, alg-geom/9606013] where the equations of this singular surface were computed, we proved that Z defines a smooth point in the appropriate Hilbert scheme and that Z cannot be smoothed in P^4. Here we consider the analogous situation in higher dimensional projective spaces P^{n-1}, where, to our surprise, the answer depends on the dimension n-1. If n is odd the union of two scrolls cannot be smoothed, whereas it can be smoothed if n is even. We construct an explicit smoothing. | |
| dc.description | LaTeX2e with theorem, amstex, amssymb, amscd packages; 11 pages | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9703009 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9703009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150284 | |
| dc.subject | Algebraic Geometry | |
| dc.title | A Remark on the Geometry of Elliptic Scrolls and Bielliptic Surfaces | |
| dc.type | text |