Focal Loci of Algebraic Varieties I
| dc.creator | Catanese, Fabrizio | |
| dc.creator | Trifogli, Cecilia | |
| dc.date | 2000-05-10 | |
| dc.date.accessioned | 2026-07-07T04:35:09Z | |
| dc.date.available | 2026-07-07T04:35:09Z | |
| dc.description | The focal locus $Σ_X$ of an affine variety $X$ is roughly speaking the (projective) closure of the set of points $O$ for which there is a smooth point $x \in X$ and a circle with centre $O$ passing through $x$ which osculates $X$ in $x$. Algebraic geometry interprets the focal locus as the branching locus of the endpoint map $ε$ between the Euclidean normal bundle $N_X$ and the projective ambient space ($ε$ sends the normal vector $O-x$ to its endpoint $O$), and in this paper we address two general problems : 1) Characterize the "degenerate" case where the focal locus is not a hypersurface 2) Calculate, in the case where $Σ_X$ is a hypersurface, its degree (with multiplicity) | |
| dc.description | 45 pages. To appear in Comm. in Alg. (volume in honour of Hartshorne's 60-th birthday) | |
| dc.identifier | https://arxiv.org/abs/math/0005096 | |
| dc.identifier | http://arxiv.org/abs/math/0005096 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59163 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 14N15;14M99;53A07;53A20 | |
| dc.title | Focal Loci of Algebraic Varieties I | |
| dc.type | text |