Some comments on K3 surfaces

I’m preparing a talk on the minimal model program with some emphasis on flops: certain birational maps that carry one between minimal models. One of the first to be constructed was the Atiyah flop, which has a pleasing toric interpretation and carries interesting consequences for moduli of K3 surfaces. K3 surfaces are the surface version of elliptic curves: smooth projective surfaces with trivial canonical bundle (and the technical constraint that the first Betti number vanishes). I have some overflow notes from those that I’m currently refining down for my talk and so I thought that I would post them here to ensure that they do not go untold!

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