Buchsbaum rings and applications: an interaction between algebra, geometry and topology

Buchsbaum Rings and Applications......Page 1
Preface......Page 4
Table of Contents......Page 6
Introduction and some examples......Page 8
§1. Local algebra and homological algebra......Page 20
§2. Graded modules and Künneth formulas......Page 32
§3. Local duality......Page 44
§4. Resolutions and duality......Page 51
§1. Characterization of Buchsbaum modules by systems of parameters......Page 61
§2. Cohomological characterization of Buchsbaum modules......Page 69
§3. Graded Buchsbaum modules......Page 94
§4. Segre products of graded Cohen-Macaulay modules......Page 98
II. Hochster-Reisner theory for monomial ideals. An interaction between algebraic geometry, algebraic topology and combinatorics......Page 105
§1. Foundations......Page 106
§2. The homological Cohen-Macaulay criterion of Reisner......Page 114
§3. The topological Cohen-Macaulay criterion of Schwartau......Page 122
§4. Further applications to algebraic topology and combinatorics......Page 131
III. On liaison among curves in projective three space......Page 154
§1. On liaison among arithmetical Buchsbaum curves in P3......Page 155
§2. On liaison addition and applications......Page 173
§3. On curves linked to lines in P3 and applications......Page 180
§4. On self-linked curves in P3......Page 191
IV. Rees modules and associated graded modules of a Buchsbaum module......Page 198
§1. Some preliminary results......Page 200
§2. The Buchsbaum property of Rees modules and associated graded modules......Page 206
§3. Blowing-up characterization of Buchsbaum modules......Page 222
§1. A Buchsbaum criterion for affine semigroup rings......Page 228
§2. Some examples related to problems of Hironaka and Seidenberg......Page 233
§3. On Buchsbaum rings obtained by glueing......Page 237
§4. Construction of Buchsbaum rings with given local cohomology......Page 241
§5. Some examples of Segre products......Page 244
Appendix. On generalizations of Buchsbaum modules......Page 251
Bibliography......Page 267
Notations......Page 281
Index......Page 283