数学研究所
学术报告
杰出访问研究员综合报告会
Speaker: Prof. Frédéric CAMPANA（洛林大学）
Inviter: 王隽永、谢松晏 副研究员
Language: English
Lecture 1
Title: Specialness, Core map, Kodaira Dimension and Fibrations
Time&Venue: 2025年4月2日 10:30-12:00 & 晨兴510
Abstract: Short introduction to specialness, core map. Basic facts on Kodaira dimension, uniruled and rationally connected manifolds and associated fibrations. Insufficiencies of Kodaira dimension. Motivating examples for orbifold bases.
Lecture 2
Title: Orbifold Bases, Geometric Invariants, Bogomolov sheaves， Special manifolds
Time&Venue: 2025年4月3日 10:30-12:00 & 晨兴510
Abstract: Orbifold pairs, invariants, orbifold bases of fibrations. Their Kodaira dimensions and link to Boogomolov sheaves. Special manifolds. Examples.
Lecture 3
Title: Iitaka's conjecture and the Core Map
Time&Venue: 2025年4月7日 14:00-15:30 & 晨兴410
Abstract: Orbifold version of Iitaka's $C_{n,m}$. Construction and uniqueness of the core map, splitting varieties into special fibres and general type orbifold bases. Functoriality properties. Multiple vs divisible fibres. Special vs weakly special manifolds. Examples.
Lecture 4
Title: Splitting of the Kobayashi pseudo-distance by the core map.
Time&Venue: 2025年4月14日 10:30-12:00 & 晨兴510
Abstract: Specialness should characterize the vanishing of the Kobayashi pseudo-distance. Orbifold Kobayashi pseudo-distance, orbifold version of Lang's conjecture for general type orbifolds. Description of the Kobayashi pseudo-distance via the core map. Abelianity conjecture for the fundamental group of special manifolds, link with hyperbolicity.
Lecture 5
Title: Arithmetic version: distribution of rational points via the core map.
Time&Venue: 2025年4月16日 10:30-12:00 & 晨兴510
Abstract: Specialness should characterize potential density of rational points. Conjectural qualitative distribution of rational points via the core map and orbifold rational points. Case of orbifold curves. Orbifold Mordell conjecture (OMC). Examples where OMC disproves the weak special conjecture, connection to the abc conjecture.
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