中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

学术报告

多复变与复几何研讨班

SCV&CG Seminar

Speaker: Prof. Daniel Barlet (Institut Élie Cartan de Lorraine)

Inviter: 周向宇 院士

Language: English

Title: The use of Cycles’ space in complex geometry

Time & Venue: 2025年11月19日（星期三）  19:00 - 20:30 & 南楼N913

Abstract:  We first recall the notion of “analytic family” of cycles we show how the existence of the Cycles’ space can be used. For instance the notion of an analytic family of fibres for a proper map is related to the notion of geometric flattening and allows to make meromorphic quotients. We shall present how integration of cohomology classes on an analytic family of fibers is used to prove Varouchas Theorem. We may also sketch the proof of Hartshorne conjecture for an hypersurface in the projective space.

Title: Intersection Theory with holomorphic parameters

Time & Venue: 2025年11月24日（星期一）19:00 - 20:30 & 南楼N913

Abstract: Presentation of relative fundamental classes and their relations with analytic families of cycles. Application to the intersection theory with holomorphic parameters in a complex manifold. All these extend also to quasi-smooth complex spaces.

Title: Non compact cycles (finite type cycles)

Time & Venue: 2025年11月25日（星期二）  10:00 - 11:30 & 南楼N913

Abstract: The main tool is the semi-proper direct image theorem which allows to construct meromorphic quotients although the Cycles’ space is infinite dimensional in this context . The study of fibres in the case of quasi-proper maps leads to study the geometric flattening in this context and to characterize as “strongly quasi-proper maps” the quasi-proper maps admitting a geometric flattening.