Unbounded negativity on rational surfaces in positive characteristic

Raymond Cheng (Columbia University)

28-Oct-2021, 22:30-23:30 (2 years ago)

Abstract: Fix your favourite smooth projective surface S and wonder: how negative can the self-intersection of a curve in S be? Apparently, there are situations in which curves might not actually get so negative: an old folklore conjecture, nowadays known as the Bounded Negativity Conjecture, predicts that if S were defined over the complex numbers, then the self-intersection of any curve in S is bounded below by a constant depending only on S. If, however, S were defined over a field of positive characteristic, then it is known that the Bounded Negativity Conjecture as stated cannot hold. For a long time, however, it was not known whether the Conjecture failed for rational surfaces in positive characteristic. In this talk, I describe the first examples of rational surfaces failing Bounded Negativity which I constructed with Remy van Dobben de Bruyn earlier this year.

algebraic geometrynumber theory

Audience: researchers in the topic


SFU NT-AG seminar

Series comments: Description: Research/departmental seminar

Seminar usually meets in-person. For online editions, the Zoom link is shared via mailing list.

Organizers: Katrina Honigs*, Nils Bruin*
*contact for this listing

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