Algebraic Geometry: Bowdoin 1985, Teil 1

3-folds abelian variety algebraic fiber space algebraic surface algebraic varieties ample assume Bk(D blow-up branch canonical ring canonical singularities Cartier divisor classification codim codimension complete intersection cone conjecture contains coprime COROLLARY curves of degree curves of genus defined deformation denote differential double cover effective divisor elliptic equations equivalent example exists fibration fibre finite formula genus g geometric genus given hence Hilbert scheme hyperelliptic hyperplane hypersurface Iitaka integer invariants Invent invertible sheaf irreducible component irreducible curves isomorphic Kawamata Kodaira dimension LEMMA Let f line bundle linear system locus minimal model moduli space nonsingular normal bundle normal surface problem projective variety proof PROPOSITION proved Q-divisor quotient singularities rank rational curve resolution resp result sheaf Springer-Verlag subset subspace subvariety surjective terminal singularities theory theta functions vanishing theorem vector bundle Zariski decomposition