6 papers · 1 filter
On the genus of a maximal curve
Gabor Korchmaros, Fernando Torres
Previous results on genera g of F_{q^2}-maximal curves are improved: (1) Either g\leq (q^2-q+4)/6, or g=\lfloor(q-1)^2/4\rfloor, or g=q(q-1)/2; (2) The hypothesis on the existence…
Remarks on plane maximal curves
Angela Aguglia, Gabor Korchmaros, Fernando Torres
Some new results on plane F_{q^2}-maximal curves are stated and proved. It is known that the degree d of such curves is upper bounded by q+1 and that d=q+1 if and only if the curve…
Embedding of a maximal curve in a Hermitian variety
Gabor Korchmaros, Fernando Torres
Let X be a projective geometrically irreducible non-singular algebraic curve defined over a finite field F of order . If the number of F-rational points of X satisfies the Has…
On curves covered by the Hermitian curve, II
A. Cossidente, G. Korchmaros, F. Torres
We classify, up to isomorphism, maximal curves covered by the Hermitian curve \mathcal H by a prime degree Galois covering. We also compute the genus of maximal curves obtained by…
On curves covered by the Hermitian curve
A. Cossidente, G. Korchmaros, F. Torres
For each proper divisor d of (r^2-r+1), r being a power of a prime, maximal curves over a finite field with r^2 elements covered by the Hermitian curve of genus 1/2((r^2-r+1)/d-1)…
On plane maximal curves
A. Cossidente, J. W. P. Hirschfeld, G. Korchmaros +1
The genus of a maximal curve over a finite field with r^2 elements is either g_0=r(r-1)/2 or less than or equal to g_1=(r-1)^2/4. Maximal curves with genus g_0 or g_1 have been cha…