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代数几何研讨会 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.

报告人：

代数几何国际会议

Organizer: Caucher Birkar, Artan Sheshmani

报告人：

腾冲科技论坛

腾冲科学家论坛系列活动——院士走进腾冲一中 带去科普饕餮盛宴

报告人：

Boundedness of complements for fibered Fano threefolds in positive characteristic

In this paper, we prove Shokurov's conjecture on boundedness of complements for Fano type threefold pairs (X,B) with fibration structures in large characteristics. In particular, we prove the conjecture when ?(KX+B)?0 is nef and not big in large characteristics.

报告人：Xintong Jiang

Failure of Boundedness for Generalised Log Canonical Surfaces

In this paper, we construct counterexamples to the boundedness of generalised log canonical models of surfaces with fixed appropriate invariants, where the underlying varieties can have arbitrary Kodaira dimension. This answers a question of Birkar and the first author.

报告人：Christopher Hacon, Xiaowei Jiang

Boundedness of polarized log Calabi-Yau fibrations with bounded bases

We investigate the boundedness problem for log Calabi-Yau fibrations whose bases and general fibers are bounded. We prove that the total spaces of log Calabi-Yau fibrations are bounded in codimension one after fixing some natural invariants. We also prove that the total spaces are bounded if, in addition, the irregularity of the general fibers vanishes. Then we apply our results to the boundedness problem for stable minimal models and fibered Calabi-Yau varieties.

报告人：Xiaowei Jiang, Junpeng Jiao, Minzhe Zhu

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 ...

报告人：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.

报告人：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.

报告人：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.

报告人：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.

报告人：Caucher Birkar