Hodge-Deligne等变多项式与超平面排列的单值性
代数几何
2011-07-21 v2
摘要
我们研究了齐次多项式的Milnor纤维上单值性与Deligne混合Hodge结构之间的相互作用。在超平面排列Milnor纤维的情形下，我们得到了关于可能权重的一个新结果。对于线排列，我们以一种新方式证明了Budur和Saito的一个事实，即谱由弱组合数据决定，并表明该结果对Hodge-Deligne多项式不成立。
引用
@article{arxiv.1006.3462,
title = {Hodge-Deligne equivariant polynomials and monodromy of hyperplane arrangements},
author = {Alexandru Dimca and Gus Lehrer},
journal= {arXiv preprint arXiv:1006.3462},
year = {2011}
}
备注
An appendix is added in this second version, where we use $p$-adic Hodge theory to prove that quite generally, whenever a $\G$-variety $X$ is defined over a number field, the number of rational points of its reductions modulo prime ideals can be used in certain cases to compute the equivariant Hodge-Deligne polynomial