The Cayley Method for Studying Discriminants
In Chapter 1 we introduced, for any projective variety X ⊂ P n , the X-discriminant Δ X which is the equation of the projective dual variety X ∨ (so Δ X is a constant if X ∨ is not a hypersurface). We now explain the method that allows us, for a smooth X, to write down at least in principle, the polynomial Δ X . The method goes back to the remarkable paper by Cayley [Ca4] on elimination theory, in which the foundations were laid for what is now called homological algebra. The Cayley method can also be applied to other similar problems, such as finding resultants (see Chapter 3).
KeywordsVector Bundle Line Bundle Spectral Sequence Global Section Coherent Sheave
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