Complex surfaces 2: Minimal surfaces

This talk is part of a series about complex surfaces, and explains what minimal surfaces are.

A minimial surfaces is one that cannot be obtained by blowing up a nonsingular surfaces at a point. We explain why every surface is birational to a minimal nonsingular projective surface. We discuss Zariski's theorem expressing a birational map in terms of blowups and blowdowns, and state Castelnuovo's criterion for a curve to be exceptional (meaning it is the inverse image of the blowup of a point). Finally we give the birational map from P2 to P1 x P1 as an example.

[narutosaga]

This man putting out videos like a professional YouTuber!! Damn

[rhyswells]

- The end on slide timestamps are the following:
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[mydearfriend]

I most of times don't feel like studying. Can you suggest something sir?

[万庵轂]

Thanks to this video. Now, I understand why the self-intersection of an exceptional curve is -1 intuitively.