Problems on pencils of small genus
Problems on pencils of small genus
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小属铅笔问题
DOI：
10.4310/jdg/1214440435
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发表时间：
2003
影响因子：
2.5
通讯作者：
M. Reid
中科院分区：
文献类型：
--
作者：
M. Reid
设f：X → B是基曲线B上的纤维空间;对于f的纤维记为F = f−1（P），设g = genusF ≥ 2且B = genusB。对于亏格2的铅笔，Horikawa和Xiao Gang的几何方法是非常强大和实用的，我的目标是尝试将这些方法推广到亏格3，4，5，. . .本文的问题是研究f的相对标准代数R（X/B）= R（f），以及如何利用它来获取X上的地理信息。首先是定义：写KX/B = KX −fKB，并设f ∈（K X/B）= Rn，其中n ≥ 0。
Let f : X → B be a fibre space of curves over a base curve B; write F = f−1(P ) for a fibre of f , and set g = genusF ≥ 2 and b = genusB. For genus 2 pencils, the geometric methods of Horikawa and Xiao Gang are very powerful and practical, and my aim is to try to generalise these to genus 3, 4, 5,. . . My problems here are concerned with the study of the relative canonical algebra R(X/B) = R(f) of f , and how to use it to get geographical information on X. First the definitions: write KX/B = KX −fKB, and set f∗(K X/B) = Rn for n ≥ 0.