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On maximal curves in characteristic two | | Miriam Abdon
; Fernando Torres
; | | Date: |
13 Nov 1998 | | Journal: | Manuscripta Math. 99 (1999), 39--53 | | Subject: | Algebraic Geometry MSC-class: PC: 11G20, 11G, 11; SC: 14G15, 14G, 14 | math.AG | | Abstract: | The genus g of an F_{q^2}-maximal curve satisfies g=g_1:=q(q-1)/2 or gle g_2:= [(q-1)^2/4]. Previously, such curves with g=g_1 or g=g_2, q odd, have been characterized up to isomorphism. Here it is shown that an F_{q^2}-maximal curve with genus g_2, q even, is F_{q^2}-isomorphic to the nonsingular model of the plane curve sum_{i=1}^{t}y^{q/2^i}=x^{q+1}, q=2^t, provided that q/2 is a Weierstrass non-gap at some point of the curve. | | Source: | arXiv, math.AG/9811091 | | Services: | Forum | Review | PDF | Favorites | |
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