تقرير
On the Hodge Structures of Global Smoothings of Normal Crossing Varieties
| العنوان: | On the Hodge Structures of Global Smoothings of Normal Crossing Varieties |
|---|---|
| المؤلفون: | Chen, Kuan-Wen |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry |
| الوصف: | Let $f:X \rightarrow \Delta $ be a one-parameter semistable degeneration of $m$-dimensional compact complex manifolds. Assume that each component of the central fiber $X_0$ is K\"ahler. Then, we provide a criterion for a general fiber to satisfy the $\partial\overline{\partial}$-lemma and a formula to compute the Hodge index on the middle cohomology of the general fiber in terms of the topological conditions/invariants on the central fiber. We apply our theorem to several examples, including the global smoothing of $m$-fold ODPs, Hashimoto-Sano's non-K\"ahler Calabi-Yau threefolds, and Sano's non-K\"ahler Calabi-Yau $m$-folds. To deal with the last example, we also prove a Lefschetz-type theorem for the cohomology of the fiber product of two Lefschetz fibrations over $\mathbb{P}^1$ with disjoint critical locus. Comment: 61 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.19229 |
| رقم الأكسشن: | edsarx.2404.19229 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |