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- W2949336875 abstract "Previous results on genera g of F_{q^2}-maximal curves are improved: (1) Either gleq (q^2-q+4)/6, or g=lfloor(q-1)^2/4rfloor, or g=q(q-1)/2; (2) The hypothesis on the existence of a particular Weierstrass point in cite{at} is proved; (3) For qequiv 1pmod{3}, qge 13, no F_{q^2}-maximal curve of genus (q-1)(q-2)/3 exists; (4) For qequiv 2pmod{3}, qge 11, the non-singular F_{q^2}-model of the plane curve of equation y^q+y=x^{(q+1)/3} is the unique F_{q^2}-maximal curve of genus g=(q-1)(q-2)/6; (5) Assume dim(cD_cX)=5, and char(fq)geq 5. For qequiv 1pmod{4}, qgeq 17, the Fermat curve of equation x^{(q+1)/2}+y^{(q+1)/2}+1=0 is the unique F_{q^2}-maximal curve of genus g=(q-1)(q-3)/8. For qequiv 3pmod{4}, qge 19, there are exactly two F_{q^2}-maximal curves of genus g=(q-1)(q-3)/8, namely the above Fermat curve and the non-singular F_{q^2}-model of the plane curve of equation y^q+y=x^{(q+1)/4}. The above results provide some new evidences on maximal curves in connection with Castelnuovo's bound and Halphen's theorem, especially with extremal curves; see for instance the conjecture stated in Introduction." @default.
- W2949336875 created "2019-06-27" @default.
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- W2949336875 date "2000-08-26" @default.
- W2949336875 modified "2023-10-16" @default.
- W2949336875 title "On the genus of a maximal curve" @default.
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