Conduttore e aggiunte di curve algebriche.

The present thesis contains a detailed study about blow-up of curves, adjoint curves and conductor ideals. The first two chapters are dedicated to preliminaries from Commutative Algebra and Algebraic Geometry, including a brief introduction to sheaf theory. The third is about algebraic curves and there is presented a detailed exposition of the process of blowing up. The most important result proved in this part is the resolution of singularities for irreducible curves through a finite chain of blow-ups. There is also a sketch of the generalization of blow-up to surfaces. In the fourth chapter we translate in a pure algebraic language two papers by Silvio Greco and Paolo Valabrega about adjoints and conductor, written in a more geometrical way. They present five definitions of adjoint curves, i.e. the classical one, due to Brill and Noether, the Gorenstein's definition, based on conductor ideal, the Keller's definition, using branches of singularities and the two definitions denoted by A4, A5, based on the notion of virtual multiplicity. These five notions are carefully investigated in order to decide whether they are equivalent. It turns out that four of them are, while the fifth (the classical one), anyhow strictly related to the others, can give a slightly different notion. Moreover, we describe the notions of special adjoints and true adjoins, following a paper by Anna Oneto. As an application, in chapter five we present algorithms computing the conductor ideal of an algebraic curve and testing whether a plane curve is an adjoint of a given plane curve. For these two algorithms we give a concrete implementation using the softwares Maple and Singular.