Frontmatter

Chapters in this book

1. Frontmatter I
2. Preface V
3. Contents VII
4. Zero-dimensional Schemes: Singular Curves and Rational Surfaces 1
5. Lectures
6. Duality, derivations and deformations of zero-dimensional singularities 11
7. On Higher Order Embeddings and Vector Bundles 33
8. Singular curves on surfaces and linear systems 43
9. The Strong Castelnuovo Lemma for zerodimensional schemes 53
10. Hilbert Functions of Dots in Linear General Position 65
11. Curves of maximal genus in P⁴ 81
12. Graph Curves, Colorings, and Matroids 89
13. Algorithms for constructing minimal generators of ideals of projective points in polynomial time 113
14. Some applications of Castelnuovo theory via residuation 121
15. On the injectivity of the nodal map 131
16. Syzygies of Points in Projective Space and Applications 145
17. The zero dimensional scheme defined by the intersection of two curve singularities 171
18. Sharp Bounds for the p-th Module of Syzygies of Certain Rational Surfaces 179
19. Resolutions of O-dimensional subschemes of a smooth quadric 191
20. Points in Uniform Position and Maximum Distance Separable Codes 205
21. Points in Good Position in P² 213
22. The desingularization of Hilb⁴P³ and its Betti numbers 231
23. Some applications of the canonical module of a O-dimensional scheme 243
24. Zero-dimensional Schemes on Abelian Surfaces 253
25. Hypersurface Sections of Curves 269
26. On the computation of the height of an ideal in a polynomial ring 283
27. Generators of ideals of curves: some polynomial algorithms for their computation 299
28. Remarks on Graded Integral Domains of Dimension One Over a Finite Field 307
29. Minimal polynomials and sparse resultants 317
30. Appendices
31. Open problems 325
32. List of Participants 333