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.