On the genus of a maximal curve
On the genus of a maximal curve
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关于最大曲线的亏格
DOI：
10.1007/s002080200316
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发表时间：
2000
影响因子：
1.4
通讯作者：
F. Torres
中科院分区：
文献类型：
--
作者：
G. Korchmáros;F. Torres
抽象的。本文讨论了中国植物属谱的上限和第一空区
$ \mathbf F_{q^2} $-极大曲线是已知的，参见[34]，[16]，[35]。在本文中，我们确定了第二个差距。第一间隙和第二间隙都是近似恒定的时间
$q^2$，但这并不适用于第三个差距，这只是1，
$q\equiv 2{\pmod 3}，$ while（至多）常数乘以q
$q\equiv 0.$这表明，确定第三个差距的问题，这是目前工作的对象，
$\mathbf F_{q^2}$-极大曲线可能是复杂的。在这里，我们研究一个相关的问题，即表征那些
$\mathbf F_{q^2}$-亏格等于谱中第三（或可能第四）大值的极大曲线。我们的研究结果还提供了一些新的证据，
$\mathbf F_{q^2}$-极大曲线与Castelnuovo的亏格界、Heglien定理和极值曲线的关系
Abstract. The upper limit and the first gap in the spectrum of genera of
$ \mathbf F_{q^2} $-maximal curves are known, see [34], [16], [35]. In this paper we determine the second gap. Both the first and second gaps are approximately constant times
$q^2$, but this does not hold true for the third gap which is just 1 for
$q\equiv 2{\pmod 3},$ while (at most) constant times q for
$q\equiv 0{\pmod 3}.$ This suggests that the problem of determining the third gap which is the object of current work on
$\mathbf F_{q^2}$-maximal curves could be intricate. Here, we investigate a relevant related problem namely that of characterising those
$\mathbf F_{q^2}$-maximal curves whose genus is equal to the third (or possible the forth) largest value in the spectrum. Our results also provide some new evidence on
$\mathbf F_{q^2}$-maximal curves in connection with Castelnuovo's genus bound, Halphen's theorem, and extremal curves.
有限域上的维尔斯特拉斯点和曲线
影响因子：
1.8
作者：
Karl;J. Voloch
通讯作者：
J. Voloch