论文标题
复杂的投影性超曲面的消失的同种学和贝蒂界限
Vanishing cohomology and Betti bounds for complex projective hypersurfaces
论文作者
论文摘要
我们利用消失的周期和不正正滑轮的形式主义来引入和研究复杂的投射性超曲面的消失。结果，我们给出了贝蒂（Betti）数量的投影性超曲面的上限，在孤立的奇异性情况下通过DIMCA获得了不同方法的概括，而Siersma-Tibăr在Hypersurfaces的情况下，具有$ 1 $ dimensiment的奇异界面。我们还证明了lefschetz超平面定理的Hypersurfaces的补充，该定理考虑了奇异基因座的尺寸，我们使用它来提供新的Kato结果证明。
We employ the formalism of vanishing cycles and perverse sheaves to introduce and study the vanishing cohomology of complex projective hypersurfaces. As a consequence, we give upper bounds for the Betti numbers of projective hypersurfaces, generalizing those obtained by different methods by Dimca in the isolated singularities case, and by Siersma-Tibăr in the case of hypersurfaces with a $1$-dimensional singular locus. We also prove a supplement to the Lefschetz hyperplane theorem for hypersurfaces, which takes the dimension of the singular locus into account, and we use it to give a new proof of a result of Kato.
