Reducible Hilbert scheme of smooth curves with positive Brill-Noether number
Reducible Hilbert scheme of smooth curves with positive Brill-Noether number
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正布里尔-诺特数光滑曲线的可约希尔伯特格式
DOI：
10.1090/s0002-9939-1994-1221726-3
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
C. Keem
中科院分区：
文献类型：
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作者：
C. Keem
在本文中，我们展示了具有正布里尔-诺特数的 PI 中度 d 和亏格 g 的光滑曲线方案 >'d、g、r 的各种可简化示例。具有正 p(d, g, r) 的可约 >'d, g,I 的示例，即示例 J'2g-8,g,g-8，已为某些人所知，并且似乎首先出现在 Eisenbud 和 Harris 的文献中，Irreducibility of some family of Linear Series with Brill-Noether number -1, Ann.科学。高等学校标准。高级。 (4) 22 (1989), 33-53。本文的目的是通过使用一般的 k 角曲线将更广泛的示例添加到此类可简化示例的列表中。我们还证明 'd , gr 对于 d>2g-7 和 g-d+r 的范围是不可约的
In this paper we demonstrate various reducible examples of the scheme >'d, g,r of smooth curves of degee d and genus g in PI with positive Brill-Noether number. An example of a reducible >'d, g,I with positive p(d, g, r), namely, the example J'2g-8,g,g-8, has been known to some people and seems to have first appeared in the literature in Eisenbud and Harris, Irreducibility ofsomefamilies of linear series with Brill-Noether number -1, Ann. Sci. Ecole Norm. Sup. (4) 22 (1989), 33-53. The purpose of this paper is to add a wider class of examples to the list of such reducible examples by using general k-gonal curves. We also show that 'd , gr is irreducible for therangeof d>2g-7 and g-d+r