发表机构
University of Wisconsin-Madison; Institute of Mathematics of the Romanian Academy（威斯康星大学麦迪逊分校; 罗马尼亚科学院数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究综述复多项式映射纤维上同调的已知结果，建立分岔值处消失上同调新结果，推导贝蒂数上界，将相关定理推广至含任意奇点的多项式映射。
AI 中文摘要
我们综述了复多项式映射纤维上同调的已知结果，特别强调消失范围，并建立了多项式在分岔值处的消失上同调的新结果。我们还根据局部奇点不变量推导了一般纤维与非典型纤维的首个可能非零贝蒂数的上界。这些结果将Tibăr、Siersma、Dimca等人的若干定理，从孤立奇点（包括无穷远处的奇点）的情形推广到具有任意奇点的多项式映射。
英文摘要
We recast known results on the cohomology of fibers of complex polynomial maps, with particular emphasis on vanishing ranges, and establish new results on the vanishing cohomology of a polynomial at a bifurcation value. We also derive sharp upper bounds for the first possibly nonvanishing Betti number of general and atypical fibers in terms of local singularity invariants. These results extend several theorems of Tibăr, Siersma, Dimca, and others from the case of isolated singularities, including singularities at infinity, to polynomial maps with arbitrary singularities.
Commentscomments are very welcome! v2: various remarks added, one section removed, a few calculations are corrected and enhanced, showing now that bounds are sharp
