Limit linear series, the irrationality of π_{π}, and other applications
David Eisenbud, Joe Harris Β· Bulletin of the American Mathematical Society Β· 1984
We describe degenerations and smoothings of linear series on some reducible algebraic curves.Applications include a proof that the moduli space of curves of genus g has general type for all g > 24, a proof that the monodromy action is transitive on the set of linear series of dimension r and degree d on a general curve of genus g when p := g -(r + l)(g -d+r) = 0, a proof that there exist Weierstrass points with every semigroup of a certain class-in particular, on curves of genus g, all those semigroups with weight w < g/2 occur and a proof that the monodromy group acts as the full symmetric group on the g 3 -g Weierstrass points of the general curve.