Berlin: de Gruyter, 1994. — 348 p.The International Conference on "Zero-Dimensional Schemes" was held in Ravello (Salerno) from June 8 to 13, 1992. This volume contains most of the lectures given at the Conference as well as papers grown up from discussions among participants. In addition we have inserted at the end of the volume a list of problems and questions; most of them were discussed during the conference.Contents:Preface Survey paper Zero-dimensional schemes: Singular curves and rational surfaces Duality, derivations and deformations of zero-dimensional singularities On higher order embeddings and vector bundles Singular curves on surfaces and linear systems The strong Castelnuovo lemma for zero dimensional schemes Hilbert functions of dots in linear general position Curves of maximal genus in Pi Graph curves, colorings, and matroids Algorithms for constructing minimal generators of ideals of projective points E in polynomial time Some applications of Castelnuovo theory via residuation On the injectivity of the nodal map Syzygies of points in projective space and applications The zero dimensional scheme defined by the intersection of two curve singularities Sharp bounds for the p-th module of syzygies of certain rational surfaces Resolutions of O-dimensional subschemes of a smooth quadric Points in uniform position and maximum distance separable codes Points in good position in P2 The desingularization of Hilb4 P3 and its Betti numbers Some applications of the canonical module of a O-dimensional scheme Zero-dimensional schemes on abelian surfaces Hypersurface sections of curves On the computation of the height of an ideal in a polynomial ring Generators of ideals of curves: some polynomial algorithms for their computation Remarks on graded integral domains of dimension one over a finite field Minimal polynomials and sparse resultants Appendices Open problems List of participants
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