Chern-Schwartz-MacPherson classes and the Euler characteristic of degeneracy loci and special divisors
Chern-Schwartz-MacPherson classes and the Euler characteristic of degeneracy loci and special divisors
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Chern-Schwartz-MacPherson 类以及简并位点和特殊因子的欧拉特征
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
P. Pragacz
中科院分区：
文献类型：
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作者：
A. Parusiński;P. Pragacz
这一概念覆盖了一大类有趣的变种(例如，第3节中研究的特殊因子变种)。在假设X是非奇异的和(v是适当的“一般”的)的假设下，几位作者用不同的上同调不变量和数值不变量给出了DR(9#)的欧拉特征的显式公式。例如，如果(0是向量丛的一部分，则Hirzebruch[H]和Navarro-Aznar[N]给出了欧拉特征值X(Do(Fp))的公式。如果DR(())是非奇异X中的一条曲线或曲面，Harris和Tu[H-T]用E、F和X的陈氏类给出了X(DR(V))的一些显式公式，但在额外的假设下，DR(V)=0(这意味着DR(Q)是非奇异的)。在Loc.cit中。作者还提出了在DR1(？)=0或更强的假设下寻找X(dR(？))的一般公式的问题--如果存在这样的公式！第一个问题由第二个被命名的作者[PRL，命题5.7]通过使用普遍支持的关于简并性的多项式来肯定地解决
This concept overlaps a large family of interesting varieties (for example, the varieties of special divisors studied in Section 3). Several authors have worked out explicit formulas for the Euler characteristic of Dr(9#) in terms of different cohomological and numerical invariants under the assumption that X is nonsingular and (v is appropriately "general". For instance, if (0 is a section of a vector bundle, then the formulas for the Euler characteristic X(Do(fp)) were given by Hirzebruch [H] and Navarro-Aznar [N]. If Dr(() is a curve or a surface in a nonsingular X, some explicit formulas for X(Dr(V)) were given by Harris and Tu [H-T] in terms of the Chern classes of E, F and X, but under the extra assumption Dr,1 (v) = 0 (which implies that Dr(Q) is nonsingular). In loc.cit. the authors also posed the problem of finding a general formula for X(Dr(?O))-if such exists!-under the assumption Dr 1 (() = 0 or, even stronger, without this assumption. The first problem was solved positively by the second named author [Prl, Proposition 5.7], by the use of polynomials universally supported on degeneracy