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Matthew Stover : Positive combinations of negative curves on surfaces.

Let S be a smooth projective surface over a field k. If S contains sufficiently many curves of nonpositive self-intersection, we show that that there are two such curves C_1, C_2 and positive integers a, b so that aC_1 + bC_2 has positive self-intersection. I will then describe some applications of this result to the geometry and topology of complex projective surfaces uniformized by the unit ball or the product of two Poincare disks. This is joint with Ted Chinburg.

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