Betti numbers of hypersurfaces and defects of linear systems
Betti numbers of hypersurfaces and defects of linear systems
复制标题
超曲面的贝蒂数和线性系统的缺陷
DOI：
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发表时间：
1990
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影响因子：
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通讯作者：
A. Dimca
中科院分区：
文献类型：
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作者：
A. Dimca
0.导论.令w（Wo，…，wn）是整数正权重的集合，并且由S表示由条件deg（x）wt对0，n分次的多项式环C[X 0，xn]。对于任意分次对象M，设Mk表示k次齐次分量。设fSN是关于w的N次加权齐次多项式。设V是加权射影空间P（w）Proj S Cn+1\{0}/C* 中由f 0定义的超曲面，其中C+1上的C*-作用由t.x（tWx 0，...，W“xn）对于C*，xC+。假设f的奇异轨迹E（f）是一维的，即
0. Introduction. Let w (Wo,..., wn) be a set of integer positive weights and denote by S the polynomial ring C[Xo, xn] graded by the conditions deg(x) wt for 0, n. For any graded object M, let Mk denote the homogeneous component of degree k. Let f SN be a weighted homogeneous polynomial of degree N with respect to w. Let V be the hypersurface defined by f 0 in the weighted projective space P(w) Proj S Cn+l\{0}/C* where the C*-action on C+1 is defined by t.x (tWxo,..., W"xn) for C*, x C+. Assume that the singular locus E(f) of f is 1-dimensional, namely