Contents Part 1. Nonexistence and Existence 1 Chapter 1. Introduction 3 Chapter 2. Numerical Conditions 7 Chapter 3. Homological Methods 13 Chapter 4. Some Refinements 27 Chapter 5. Constructing Artinian Level Algebras 31 5.1. Inverse Systems 31 5.2. Level Quotients of the Co-ordinate Rings of Points 37 5.3. Constructing Level Algebras with the WLP 40 5.4. The Linked-Sum Method 48 Chapter 6. Constructing Level Sets of Points 55 6.1. Method 1: Intersection of Suitable Curves 55 6.2. Method 2: Liaison Tricks 58 6.3. Method 3: Union of suitable sets of points 62 6.4. Method 4: General Sets of Points on Suitable curves 64 Chapter 7. Expected Behavior 67 Part 2. Appendix: A Classification of Codimension Three Level Algebras of Low Socle Degree 73 Appendix A. Introduction and Notation 75 Appendix B. Socle Degree 6 and Type 2 77 Appendix C. Socle Degree 5 93 Appendix D. Socle Degree 4 119 Appendix E. Socle Degree 3 129 Appendix F. Summary 133 Appendix. Bibliography 137
Previous Page Next Page