Characteristic classes of discriminants and enumerative geometry
Characteristic classes of discriminants and enumerative geometry
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判别式和枚举几何的特征类
DOI：
10.1080/00927879808826335
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发表时间：
1998
影响因子：
0.7
通讯作者：
P. Aluffi
中科院分区：
文献类型：
--
作者：
P. Aluffi
我们计算了一个非常充裕的线性系统在非奇异变异上的判别超曲面的欧拉阻塞和Mather’s Chern类。比较这个和其他特征类的余维数-1和2项，可以快速计算光滑变化上一个非常丰富的线束的尖角和双节部分的轨迹度，以及表面上线性系统的尖节轨迹度。我们还显式地计算了schwarz - macpherson地层类中三次平面曲线p9中的判别式和P1上的∣O(d)∣判别式的所有项。
We compute the Euler obstruction and Mather’s Chern class of the discriminant hypersurface of a very ample linear system on a nonsingular variety. Comparing the codimension-1 and 2 terms of this and other characteristic classes of the discriminant leads to a quick computation of the degrees of the loci of cuspidal and binodal sections of a very ample line bundle on a smooth variety, and of the, tacnodal locus for linear systems on a surface. We also compute explicitly all terms in the Schwartz-MacPherson’s classes of strata of the discriminant in the P9of of cubic plane curves, and of the discriminant of∣O(d)∣ on P1.