复拟射影簇对称积的特征类
代数几何
2012-07-25 v3
摘要
我们证明了奇异复拟射影簇的对称积的适当扭曲特征类的生成级数公式。更具体地，我们研究了关于动机系数以及混合 Hodge 模复形的同调 Hirzebruch 类。作为特例，我们得到了对称积的（相交）同调 Hirzebruch 类的生成级数公式。在某些情况下，后者导出了扭曲同调 L-类的类似公式，推广了 Hirzebruch-Zagier 和 Moonen 的结果。我们的方法也适用于研究凝聚层（复形）的 Todd 类以及可构造层（复形）的陈类，将 Moonen 和 Ohmoto 的结果分别推广到了任意系数。
关键词
引用
@article{arxiv.1008.4299,
title = {Characteristic classes of symmetric products of complex quasi-projective varieties},
author = {Sylvain E. Cappell and Laurentiu Maxim and Joerg Schuermann and Julius L. Shaneson and Shoji Yokura},
journal= {arXiv preprint arXiv:1008.4299},
year = {2012}
}
备注
Paper rewritten to also include generating series formulae for motivic homology Hirzebruch classes, Todd classes of coherent sheaves, as well as Chern classes of constructible sheaves. Some special cases of L-class formulae are also obtained. Moreover, we give a mixed-Hodge-module-free proof for the case of motivic homology Hirzebruch classes