The Basic Results of the Brill-Noether Theory
As we recalled in Chapter I, a genus g curve depends on 3g — 3 parameters, describing the so-called moduli of the curve. Our goal in this chapter is to describe how the projective realizations of a curve vary with its moduli, and what it means, from this point of view, to say that a curve is “general” or “special.” Accordingly, we would like to know, first of all, what linear series can we expect to find on a general curve and, secondly, what the subvarieties of the moduli space corresponding to curves possessing linear series of specified type look like.
KeywordsDouble Point General Curve Linear Series Smooth Plane Bibliographical Note
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