Multisingularities, cobordisms, and enumerative geometry
Multisingularities, cobordisms, and enumerative geometry
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DOI：
10.1070/rm2003v058n04abeh000642
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发表时间：
2003-08
影响因子：
0.9
通讯作者：
M. Kazarian
中科院分区：
文献类型：
--
作者：
M. Kazarian
本文给出了全纯映射多奇异性圈的对偶特征类用剩余多项式表示的一个普适公式。这样一个普遍公式的存在性定理将托姆多项式的存在性定理推广到了多奇异性的情形。一个类似的勒让德奇点的情况下，这个公式给出。计算了低余维奇异点的残差多项式。特别是，该公式的应用给出了推广的情况下，经典的结果Plucker和鲑鱼计数的奇点相切的光滑超曲面在射影子空间。
In this paper a universal formula is given for the characteristic classes dual to the cycles of multisingularities of holomorphic maps in terms of the so-called residual polynomials. The existence theorem of such a universal formula generalizes the existence theorem for the Thom polynomial to the case of multisingularities. An analogue of this formula for the case of Legendre singularities is given. The residual polynomials of singularities of low codimension are computed. In particular, applications of the formula give generalizations to the case of the classical results of Plucker and Salmon on enumeration of singularities of tangency of a smooth hypersurface in to projective subspaces.