A small suggestion : the deformation to the normal cone is a nice construction that I would have liked to see in a first course. It illustrate the use of blow-ups, the degeneration of a family with constant fibers (an highly non-obvious concept the first times you see it) and how important intuitions from differential geometry - tubular neighbourhood neighbourhoods - have a non-trivial translation to algebraic geometry.
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A small suggestion : the deformation to the normal cone is a nice construction that I would have liked to see in a first course. It illustrate the use of blow-ups, the degeneration of a family with constant fibers (an highly non-obvious concept the first times you see it) and how important intuitions from differential geometry - tubular neighbourhood - have a non-trivial translation to algebraic geometry. |
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