How to count a single curve

Okke van Garderen (University of Glasgow)

Wednesday 13th November 16:00-17:00 Maths 311B


One of the classical ways to understand varieties is by counting their subvarieties, such as embedded rational curves. Often this only provides a very rough invariant of the variety, as is the case with simple threefold flopping contractions:  these are varieties that each contain just a single rational curve, but nevertheless have very interesting local structure. Instead, one considers Donaldson-Thomas invariants, which count sheaves supported on these curves. In this talk I will show how one can construct these invariants, and discuss some preliminary results for flops.

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