单参数光滑与拟半可态的消失循环束 退化

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

摘要翻译：
研究了复解析空间单参数光滑化的消失圈，证明了其最高次的逆上同调簇上的权滤波与单子滤波相当接近，从而使其分次片具有修正的Lefschetz分解。利用常束的逆上同调束上的加权滤波来描述它的本原部分。作为推论，我们在局部完全交情形下证明了1不是约化Milnor上同调上任意点的单同调的特征值当且仅当全空间和奇异光纤都是有理同调流形。引入了准半可退化，并通过构造加权谱序列计算了极限混合Hodge结构。作为推论，我们证明了与任意两个非常充足的线束的张量积相关联的Lefschetz铅笔的消失圈空间的非平凡性，但偶数维射影空间的情形除外，其中两个必须由三个代替。
---
英文标题：
《Vanishing cycle sheaves of one-parameter smoothings and quasi-semistable
  degenerations》
---
作者：
Alexandru Dimca, Morihiko Saito
---
最新提交年份：
2010
---
分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--

---
英文摘要：
  We study the vanishing cycles of a one-parameter smoothing of a complex analytic space and show that the weight filtration on its perverse cohomology sheaf of the highest degree is quite close to the monodromy filtration so that its graded pieces have a modified Lefschetz decomposition. We describe its primitive part using the weight filtration on the perverse cohomology sheaves of the constant sheaves. As a corollary we show in the local complete intersection case that 1 is not an eigenvalue of the monodromy on the reduced Milnor cohomology at any points if and only if the total space and the singular fiber are both rational homology manifolds. Also we introduce quasi-semistable degenerations and calculate the limit mixed Hodge structure by constructing the weight spectral sequence. As a corollary we show non-triviality of the space of vanishing cycles of the Lefschetz pencil associated with a tensor product of any two very ample line bundles except for the case of even-dimensional projective space where two has to be replaced by three.
---
PDF链接：
https://arxiv.org/pdf/0810.4896

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：单参数 Constructing Generations composition Dimensional case 推论 参数 情形 了准