China Southeastern Algebraic Geometry Symposium VII
第七届东南代数几何研讨会
Home Schedule Directions Flyer
12/07
8:50–9:00 Registration
9:00–10:00 An introduction to Bridgeland stability condition, I
Chunyi Li

At the beginning of this century, inspired by the theories of physicist Douglas, Bridgeland introduced the concept of stability conditions on triangulated categories and proved an important foundational theorem, namely that all stability conditions form a complex manifold. Over the past two decades, this theory has found numerous applications in various fields, including algebraic geometry, enumerative geometry, representation theory, category theory, and symplectic geometry.

In this series of four talks, we will start with the slope stability of vector bundles on complex algebraic curves and progress to some recent developments at the forefront of this field. The introductory content is expected to include the following: Slope stability on curves and polarized varieties, King's stability on quiver, Beilinson quiver, triangulated category, bounded derived category of coherent sheaves, Bounded t-structure and slicing. Stability condition and stability manifold, Wall and chamber structure, stability condition on curves. Bogomolov inequality, tilting pair, stability condition on surfaces. Bayer–Macri divisor, Wall-crossing, strange duality.

10:00–10:20 Group Photo, Coffee & Tea Break
10:20–11:20 Uncountablity incentive in deformation theory
Sheng Rao
I will report mainly the progress on deformation limit and invariance of plurigenera of Moishezon manifolds over the unit disk. In particular, the role of uncountable distribution therein will be explained. If time permits, I will report one recent rigidity result of hyperbolic manifolds under the uncountable distribution condition. This talk is based on several joint works with Mu-Lin Li, I-Hsun Tsai, Kai Wang and Meng-jiao Wang.
11:20–11:30 Coffee & Tea Break
11:30–12:30 An introduction to Bridgeland stability condition, II
Zhiyu Liu
Noon Lunch
14:30–15:30 An introduction to Bridgeland stability condition, III
Chunyi Li
15:30–16:00 Coffee & Tea Break
16:00–17:00 On the cohomological representations of a finite automorphism group of a nodal curve
Wenfei Liu
We study the tame action of a finite automorphism group \(G\) of a nodal curve \(C\) on the cohomology groups of a \(G\)-equivariant sheave \(F\), either coherent or locally constant, and give formulas of Chevalley–Weil type. The focus is on the case where \(C\) is stable, and \(F\) is a pluricanonical sheaf or the locally constant sheaf. In this case, we may draw several basic conclusions from the Chevalley–Weil type formulas such as the faithfulness of the \(G\)-action on cohomology groups. Some new phenomena, pathological compared to the smooth curve case, are discussed. As applications, we use our formulas to compute the deformation space of the pair \((C, G)\) and the invariants of nonnormal product-quotient surfaces \((C\times D)/G\), where \(C\) and \(D\) are stable curves and \(G\) acts diagonally on \(C\times D\). The talk is based on a joint work with 刘青.
18:00 Banquet
12/08
09:00–10:00 An introduction to Bridgeland stability condition, IV
Zhiyu Liu
10:00–10:20 Coffee & Tea Break
10:20–11:20 Minimal currents and the Abundance conjecture
Vladimir Lazić
The Abundance conjecture predicts that on a minimal projective klt pair \((X,D)\), the adjoint divisor \(K_X+D\) is semiample. In this talk, I will explain how currents, and in particular currents with minimal singularities, play a role in recent progress towards a proof of the Abundance conjecture for minimal klt pairs with non-vanishing Euler-Poincaré
11:20–11:30 Coffee & Tea Break
11:30–12:30 Bridgeland stability conditions on fibred threefolds
Hao Sun
In this talk, we will give a new conjectural construction of stability conditions on the derived category of fibred threefolds. The construction depends on a conjectural Bogomolov-Gieseker type inequality for certain stable complexes. We prove the conjectural Bogomolov-Gieseker type inequalities for ruled threefolds. It gives a type of strong Bogomolov inequality.
Noon Lunch
14:30–15:30 On structures and discrepancies of klt Calabi–Yau pairs
Junpeng Jiao
In this talk I will show that the discrepancies of log centers of all klt Calabi–Yau varieties with fixed dimension are in a finite set. I also show how minimal model program facilitates to construct rationally connected fibration structures on log Calabi–Yau pairs. This provides an alternative proof of Cao–Höring's structure theorem for Calabi–Yau cases.
15:30–17:30 Free Discussion