Embedding of a maximal curve in a Hermitian variety
| dc.creator | Korchmaros, Gabor | |
| dc.creator | Torres, Fernando | |
| dc.date | 1999-11-08 | |
| dc.date.accessioned | 2026-07-07T05:31:28Z | |
| dc.date.available | 2026-07-07T05:31:28Z | |
| dc.description | Let X be a projective geometrically irreducible non-singular algebraic curve defined over a finite field F of order $q^2$. If the number of F-rational points of X satisfies the Hasse-Weil upper bound, then X is said to be F-maximal. For a point P_0\in X(F), let πbe the morphism arising from the linear series D:=|(q+1)P_0|, and let N:=dim(D). It is known that N\ge 2 and that πis independent of P_0 whenever X is F-maximal. The following theorems will be proved: Theorem 0.1: If X is F-maximal, then π:X\to π(X) is a F-isomorphism. The non-singular model π(X) has degree q+1 and lies on a Hermitian variety defined over F of P^N(\bar F); Theorem 0.2: If X is F-maximal, then it is F-isomorphic to a curve Y in P^M(\bar F), with 2\le M\le N, such that Y has degree q+1 and lies on a non-degenerate Hermitian variety defined over F of ¶^M(\bar F). Furthermore, Aut_F(X) is isomorphic to a subgroup of the projective unitary group PGU(M+1,q^2); Theorem 0.3: If X is F-birational to a curve Y embedded in P^M(\bar F) such that Y has degree q+1 and lies on a non-degenerate Hermitian variety defined over F of P^M(\bar F), then X is F-maximal and X is F-isomorphic to Y. | |
| dc.description | 18 pages, LaTex2e | |
| dc.identifier | https://arxiv.org/abs/math/9911043 | |
| dc.identifier | http://arxiv.org/abs/math/9911043 | |
| dc.identifier | Compositio Math. 128 (2001), 95--113 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79358 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | PC: 11G20, 11G, 11; SC: 14G15, 14G, 14 | |
| dc.title | Embedding of a maximal curve in a Hermitian variety | |
| dc.type | text |