On Noether's inequality for stable log surfaces

On Noether's inequality for stable log surfaces

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Wenfei Liu , Xiamen University
Fine Hall 322

In this talk I report on some recent progress on the geography problem of stable log surfaces. This is about restrictions on their holomorphic invariants, such as the volume K^2 and the geometric genus p_g. Compared to the case of surfaces of general type, a new feature here is that the volume of a stable log surface is not necessarily an integer. Extending the work of Tsunoda and Zhang in the nineties, I will give an optimal lower bound of the volume when the geometric genus is one. Then I will use an example to illustrate that a speculated Noether type inequality for stable log surfaces does not hold in general.