Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 陈家明 博士，Université de Lorraine
| | Inviter: | | Title:
| Atypical Intersections For Variations of Hodge Structures | Time & Venue:
| 2021.04.16 16:00-17:00 南楼N204 腾讯会议：428 887 155 | Abstract:
| Given a polarizable integral variation of Hodge structure (VHS) on a smooth complex quasi-projective variety S, the associated Hodge locus is the subset of points of S for which the corresponding fiber admits more Hodge tensors than the very general fiber. A classical result of Cattani, Deligne and Kaplan states that this Hodge locus is a countable union of closed irreducible algebraic subvarieties of S, called the special subvarieties of S for the VHS. In this series of talks, I will first introduce a set of conjectures formulated by Bruno Klingler concerning the structure of this Hodge locus in terms of atypical intersections, which generalize the Zilber-Pink conjectures in the Shimura case. Then I will focus on a geometric part of these conjectures concerning the distributions of positive dimensional special subvarieties of S. More precisely, I will show that (1) there are only finitely many maximal "Hodge-theoretic rigid" special subvarities of S of Shimura type with dominant period maps, which generalizes previous results of Clozel-Ullmo and Ullmo in the Shimura case. (2) (joint work with Richard Rodolphe and Emmanuel Ullmo) if the union of horizontal (weakly) special subvarities of S is dense in S, then the period imagewill be essentially a product (of a locally symmetric variety with another period image). The techniques involved will be a combination of o-minimality and homogeneous dynamics.
| |
| |
优惠券领取后72小时内有效，10万种最新考研考试考证类电子打印资料任你选。涵盖全国500余所院校考研专业课、200多种职业资格考试、1100多种经典教材，产品类型包含电子书、题库、全套资料以及视频，无论您是考研复习、考证刷题，还是考前冲刺等，不同类型的产品可满足您学习上的不同需求。 ...考试优惠券 本站小编 Free壹佰分学习网 2022-09-19