论文标题
克莱门斯歧管的偏振
Polarized Hodge Structures for Clemens Manifolds
论文作者
论文摘要
令$ x $为calabi-yau三倍。 Conifold Transition First沿着与正常的$（-1，-1）$的普通捆绑符合$ x $合同，然后将所得的单数复杂空间$ \ bar {x} $平滑至新的紧凑型复杂歧管$ y $。这样的$ y $称为clemens歧管，可以是非kähler。我们证明，任何小的平滑$ y $ of $ \ bar {x} $满足$ \ partial \ bar {\ partial} $ - lemma。我们还表明，由杯子产品两极分化的$ h^3（y）$上的重量三的纯猪结构。这些结果回答了R. Friedman的一些问题。
Let $X$ be a Calabi-Yau threefold. A conifold transition first contracts $X$ along disjoint rational curves with normal bundles of type $(-1,-1)$, and then smooth the resulting singular complex space $\bar{X}$ to a new compact complex manifold $Y$. Such $Y$ is called a Clemens manifold and can be non-Kähler. We prove that any small smoothing $Y$ of $\bar{X}$ satisfies $\partial\bar{\partial}$-lemma. We also show that the resulting pure Hodge structure of weight three on $H^3(Y)$ is polarized by the cup product. These results answer some questions of R. Friedman.
