Transcendental base-point freeness and minimal models for projective varieties

The minimal model program for generalized pairs has become one of the fundamental tools for classifying higher dimensional algebraic varieties since its inception due to Birkar and Zhang. In this talk I will introduce an analytic version of generalized pairs, namely a triplet (X, B, T), where X is an analytic variety, B a boundary divisor and T is a bi-degree (1,1) current. The current T is the analog of a b-divisor which appears in the generalized pairs of Birkar and Zhang. We will then see that many expected results of MMP, e.g. the results parallel to BCHM still hold in this generality. Finally, as an application of this kind of MMP we will show that the transcendental base-point free theorem holds for projective varieties, which says that if X is a projective manifold and \alpha is a (1,1) Bott-Chern cohomology class on X such that \alpha-K_X is nef and big (in the analytic sense), then there is a projective morphism f:X \to Y to a normal compact Kahler variety Y and a Kahler form \omega_Y such that \alpha=f^*\omega_Y.

Speaker：Omprokash Das (Tata Institute of Fundamental Research)

Pluricanonical fibrations and automorphism groups of compact complex manifolds

Let X be a compact complex manifold, and let Y be the image of its pluricanonical map. According to a theorem due to Deligne and Ueno, the image of the automorphism group of X in the automorphism group of Y is finite if X is Moishezon. I will discuss an approach to possible generalizations of this result for the case of arbitrary compact complex manifolds. The talk is based on a joint work with Konstantin Loginov.

Speaker：Constantin Shramov (HSE University)

Minimal Surfaces and Alternating Multi-Zetas

Time: 15:30-16:30Venue: Lecture Hal B725, Shuangqing Complex Building A (清华大学双清综合楼A座B725报告厅)Zoom Meeting ID: 262 865 5007Passcode: YMSC

Speaker：Lynn Heller (BIMSA)

Curves of genus three and Picard modular forms

Time: 15:30-16:30 / Venue: Tsinghua West Stepping Classroom / Zoom Meeting ID: 455 260 1552 / Passcode: YMSC

Speaker：Gerard van der Geer (University of Amsterdam)

Topology of real algebraic curves

Time: 15:30-16:30 / Venue: Tsinghua West Stepping Classroom / Zoom Meeting ID: 455 260 1552 / Passcode: YMSC

Speaker：Ilia Itenberg (Institut de mathématiques de Jussieu - Paris Rive Gauche)

Ball quotients and moduli spaces

Time: 15:30-16:30 / Venue: Tsinghua West Stepping Classroom / Zoom Meeting ID: 455 260 1552 / Passcode: YMSC

Speaker：Klaus Hulek (Universität Hannover)

Algebraic Geometry Workshop

This conference aims to review recent advances in algebraic geometry. We seek to establish connections through related topics to promote further collaboration between these areas.

Speaker：

Conference on Algebraic Geometry

This conference aims to review recent advances in algebraic geometry. We seek to establish connections across various areas such as birational geometry, moduli theory, enumerative geometry, and related topics, with the goal of promoting further collaboration between these areas.

Speaker：

A Celebration of Fano Varieties and Singularities

The purpose of this workshop is to celebrate the final day of the Tsinghua seminar series on Fano varieties and singularities and related topics.

Speaker：

Moduli Spaces in Mathematics Workshop & Conference

Workshop:4-5 April 2023Organisers：Jungkai Chen, Keiji Oguiso, De-Qi ZhangTime：2023.4.4-2023.4.5 Speakers: ·Caucher Birkar（Tsinghua University）·János Kollár（Princeton University UTC-4）·Yongnam Lee（KAIST UTC+9）·Shigeru Mukai（Kyoto University UTC+9） / Conference:6-7 April 2023Organisers：Caucher Birkar, Ivan FesenkoTime： 2023.4.6-2023.4.7

Speaker：

Workshop on Algebraic Geometry

Organizer: Caucher Birkar, Artan Sheshmani

Speaker：

Tengchong Science and Technology Forum

Speaker：

Birational Geometry I (2026)

任课教师 Speaker: Caucher Birkar时间 Time: Every Friday 13:30-15:05 2026-02-27 ~ 06-12地点 Venue: Lecture Hall B725, Shuangqing Complex Building A (清华大学双清综合楼A座B725报告厅)Notes: https://cloud.tsinghua.edu.cn/f/fbfdc137d7e64a45959a/ 课程描述 DescriptionThis year-long course is an introduction to birational geometry, a central area of algebraic geometry.The aim is to introduce some of...

Speaker：Caucher Birkar

Birational Geometry I (2024)

任课教师 Speaker: Caucher Birkar时间 Time: Every Friday 13:30-15:05 2024-9-13 ~ 12-27地点 Venue: Lecture Hal B725, Shuangqing Complex Building A (清华大学双清综合楼A座B725报告厅)Notes: https://cloud.tsinghua.edu.cn/f/fbfdc137d7e64a45959a/ 课程描述 DescriptionThis year-long course is an introduction to birational geometry, a central area of algebraic geometry.The aim is to introduce some of t...

Speaker：Caucher Birkar

Explicit birational geometry

Schedule：Tuesdays & Thurdays, 9:50-11:25 am, May 7-July 11,2024 / Venue：Lecture Hal B725, Shuangqing Complex Building A / Date：2024-05-07~2024-07-11

Speaker：Florin Ambro (Institute of Mathematics of the Romanian Academy)

Optimal upper bounds for anti-canonical volumes of singular toric Fano varieties

Fix two positive integers d≥3 and q. We give an upper bound for anti-canonical volumes of d-dimensional 1q-lc toric Fano varieties, which corresponds to an upper bound for the dual normalized ...

Speaker：Yu Zou

Sheaf stable pairs, Quot-schemes, and birational geometry

In this paper we build bridges between moduli theory of sheaf stable pairs on one hand and birational geometry on the other hand. We will in particular treat moduli of sheaf stable pairs on smooth projective curves in detail and present some calculations in low degrees. We will also outline problems in various directions.

Speaker：Caucher Birkar, Jia Jia, Artan Sheshmani

On the cone conjecture for certain pairs of dimension at most 4

In this paper, by running MMP and considering the anti-canonical fibration, we prove the Morrison-Kawamata cone conjecture for klt Calabi-Yau pairs (X,Δ) such that dim X is at most 4, and the Iitaka dimension κ(X,−K_X) is at least dimX−2.

Speaker：Fulin Xu

Singularities on Fano fibrations and beyond

In this paper we investigate singularities on fibrations and related topics. We prove a conjecture of Shokurov and McKernan on singularities on Fano type fibrations and a conjecture of the author on singularities on log Calabi-Yau fibrations. From these we derive a variant of a conjecture of McKernan and Prokhorov on rationally connected varieties with nef anti-canonical divisor. We discuss other applications including existence of bounded klt complements and gonality of fibres of del Pezzo fibrations. We prove a general result on controlling multiplicities of fibres of certain fibrations (not necessarily of Fano type) which is the key ingredient of the proofs of the above results.

Speaker：Caucher Birkar

Moduli of algebraic varieties

We develop a moduli theory of algebraic varieties and pairs of non-negative Kodaira dimension. We define stable minimal models and construct their projective coarse moduli spaces under certain natural conditions. This can be applied to a wide range of moduli problems in algebraic geometry.

Speaker：Caucher Birkar

Seminar series on Fano varieties, singularities, and related topics

Time：Every Thursday, 7 March - 23 May, 2024 / Zoom Meeting ID: 262 865 5007 / Passcode: YMSC

Speaker：