**Beijing Algebraic Geometry Colloquium****Algebraic Geometry Activities in China**Site under construction...

Kevin Tucker

(UIC)

Bertini Theorems for F-signature

09:00 – 10:00

In characteristic zero, it is well known that multiplier ideals and log terminal singularities satisfy Bertini-type theorems for hyperplane sections. In characteristic p > 0, the analogous statements for test ideals are more complicated: while F-regular singularities satisfy Bertini, the test ideal does not. In this talk, I will describe joint work with Karl Schwede and Javier Carvajal-Rojas showing that the F-signature – a numerical invariant of singularities that detects F-regularity – satisfies the relevant Bertini statements for hyperplane sections. In particular, one can view this as a generalization of the corresponding results for F-regularity.

Roberto Svaldi

(Cambridge)

Log birational boundedness of Calabi-Yau pairs

10:30 – 11:30

I will discuss new results towards the birational boundedness of Calabi-Yau pairs. Recent work in the minimal model program suggests that pairs with trivial log canonical class should satisfy some boundedness properties.

I will show that 4-dimensional Calabi-Yau pairs which are not birational to a product are indeed log birationally bounded. This implies birational boundedness of elliptically fibered Calabi-Yau manifolds with a section, in dimension up to 5. This is joint work with Gabriele Di Cerbo.

Xuanyu Pan 潘宣余

(AMSS, CAS)

Cycles on Fano manifolds

11:45 – 12:45

In this talk, I will give a survey about cycles on Fano manifolds including a recent joint work with Cristian Minoccheri. The philosophy is that the positivity of the tangent bundle implies the simplicity of the cycle relations. At the end of this talk, I will talk about some speculation on 1-cycles on Fano manifolds.

**Organized by**Baohua Fu

Xiaotao Sun

Chenyang Xu

Qizheng Yin

**Past Meetings**

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Beijing Algebraic Geometry Colloquium

Algebraic geometry activities in Beijing.

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