## Algebraic Geometry Seminar

Feng Hao

Purdue

The Weak Bounded Negativity Conjecture

**Abstract:**In this talk I will give a proof of the Weak Bounded Negativity Conjecture, which says that given any complex smooth projective surface, for any reduced curve $C$ in $X$ and integer $g$, assume that the geometric genus of each component of $C$ is bounded from above by $g$, then the self-intersection number $C^2$ is bounded from below. The Weak Bounded Negativity Conjecture is motivated by the old folklore Bounded Negativity conjecture, which says that given any complex smooth projective surface, the self-intersection number of any reduced curve is bounded from below. Also, the Bounded Negativity Conjecture has an interesting relation with the Nagata conjecture. I will introduce those background before the proof of the Weak Bounded Negativity Conjecture. Also, I will give some further thoughts towards the Bounded Negativity Conjecture.

Wednesday October 11, 2017 at 4:00 PM in SEO 427