Curves of maximal genus in P^5
| dc.creator | Ferraro, Rita | |
| dc.date | 2001-05-18 | |
| dc.date | 2001-05-21 | |
| dc.date.accessioned | 2026-07-07T04:41:46Z | |
| dc.date.available | 2026-07-07T04:41:46Z | |
| dc.description | Let C be a reduced, irreducible, not degenerate curve, not contained on surfaces of degree <s; when d=deg(C) is large with respect to s, the arithmetic genus p_a(c) is bounded by a function G(d, r, s) which is of type d^2/2s+O(d). The existence of such a bound for curves in P^3 was announced by Halphen in 1870 and proved by Gruson and Peskine in 1978; for curves in P^r, r>3, the bound is stated and proved by Chiantini, Ciliberto and Di Gennaro in 1993. The bound is sharp, at least for d sufficiently large (Chiantini-Ciliberto- Di Gennaro give examples of extremal curves for d large, that are in general singular). The classification and the existence of curves of genus G(d, r, s) is known for r=3 and d>s^2-s (Gruson and Peskine), and for r=4 and d> 12s^2 (Chiantini and Ciliberto in 1994). In this paper the author gives the classification for the curves of maximal genus for r=5, d as in the paper of Chiantini-Ciliberto-Di Gennaro, and s>8, and proves the existence of {\it smooth} curves of maximal genus G(d, 5, s) for every d and s. With the same techniques used for the classification in P^5 it is possible to classify curves in P^r of maximal genus G(d, r, s) for every r and s>2r-2. In math.AG/0105094 the author has given an example of the classification procedure and of the costruction of smooth extremal curves in P^r. | |
| dc.description | Latex, 25 pages. Revised version, the Introduction in the submitted version was misprinted | |
| dc.identifier | https://arxiv.org/abs/math/0105158 | |
| dc.identifier | http://arxiv.org/abs/math/0105158 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61496 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14Hxx, 14M06, 14M07, 14N99 | |
| dc.title | Curves of maximal genus in P^5 | |
| dc.type | text |