论文标题
通过实际对数几何形状数量的贝蒂数量数量
Betti numbers of real semistable degenerations via real logarithmic geometry
论文作者
论文摘要
让$ x \ rightArrow c $与平滑的真实曲线$ c $一起使用简并纤维$ x_0 $。假设从共同体的角度来看，$ x_0 $的不可约组件很简单，我们就复杂的变性几何形状来为单个真正光滑纤维的单个betti数字绑定。这概括了通过组合技术获得的Renaudineau-Shaw的先前工作，用于光滑的感谢您的热带曲面。主要的新成分是使用真实对数的几何形状，它允许使用不一定是曲折的变性。
Let $X\rightarrow C$ be a totally real semistable degeneration over a smooth real curve $C$ with degenerate fiber $X_0$. Assuming that the irreducible components of $X_0$ are simple from a cohomological point of view, we give a bound for the individual Betti numbers of a real smooth fiber near $0$ in terms of the complex geometry of the degeneration. This generalizes previous work of Renaudineau-Shaw, obtained via combinatorial techniques, for tropical degenerations of hypersurfaces in smooth toric varieties. The main new ingredient is the use of real logarithmic geometry, which allows to work with not necessarily toric degenerations.
