【Course Introduction】
Course Dates: Jun. 16 - 20, 2025
Teaching Hours: 8:30 am- 12:00 pm
Course Venue: Lecture Hall 644, Lei Jun Science and Technology Building
【Course Overview】
Speaker: Vladimir Lazić, Universität des Saarlandes, Germany
Title: The Abundance conjecture
Abstract: This is a course on the Abundance conjecture, which is one of the most important conjectures in complex algebraic geometry. The conjecture predicts that some multiple of the canonical bundle on a minimal projective variety is semiample, and thus defines a morphism to another projective variety. I will give a short overview of the conjecture and the ingenious proof on threefolds by Miyaoka and Kawamata, and then present a new strategy to attack the conjecture in higher dimensions, developed together with Thomas Peternell.
The topics include:
* a semiampleness theorem by Gongyo and Matsumura
* a Nonvanishing criterion
* Abundance for semipositive canonical bundles and nonvanishing Euler-Poincaré characteristic
* currents with minimal singularities and the reformulation of the Abundance conjecture as a statement on multipler ideals
* supercanonical currents as a tool towards the proof of the Abundance conjecture
* Abundance beyond pairs: (a) nef line bundles on K-trivial varieties, (b) Generalised Abundance conjecture
Speaker: Wenhao Ou, Academy of Mathematics and Systems Science, CAS
Title: The Birational Geometry of Kähler Manifolds
Abstract: Birational geometry is a fundamental branch of algebraic geometry, primarily focused on classifying projective manifolds up to birational equivalence. A key theory developed within this framework is the Minimal Model Program (MMP). In the decade following the groundbreaking work "BCHM" in 2010, birational geometry has seen rapid advancements and has been applied to various areas of algebraic geometry.
In the context of complex geometry, Kähler manifolds serve as a more classical and natural subject of study, forming a strictly larger class that contains projective manifolds. Over the past decade, significant progress has been made in understanding and developing the birational geometry of Kähler manifolds. In particular, in the three-dimensional case, the Kähler Minimal Model Program has now been fully established.
This course aims to introduce the latest developments in this field and discuss the current open problems.
【Registration Process and Contact Information】
1. Registration and Admission Method: Click here to submit a registration application. （Except for invited speakers, all participants, including students from Wuhan University, are required to complete the registration. Applicants for the course are required to upload their personal research resumes and letters of recommendation. The letters of recommendation can also be sent to: tmcc@whu.edu.cn.）The organizing committee will select the applicants and make final admission decision. The total number of young teachers, postdocs, doctoral students, master's students, and undergraduates from other universities shall not exceed 20.
2. Registration Deadline: May 15, 2025. We will notify the admitted participants via email before May 25.
3. Funding Instructions: Accommodation will be arranged for the admitted participants from other universities in these courses. The accommodation location will be notified separately, with two students sharing one room. The accommodation costs for students will be covered by the organizing committee, but the accommodation costs of young teachers and postdocs need to be paid by themselves. The organizing committee will provide meal subsidies for non-Wuhan University admitted participants. The meal location and the form of subsidy are to be determined. The admitted participants from Wuhan University will not be eligible for the funding.
4. Contact: Lingling Tang, tmcc@whu.edu.cn, 027 - 87287715
