Noncommutative Curves of Genus Zero.

Intro -- Contents -- Introduction -- Chapter 0. Background -- 0.1. Notation -- 0.2. One-parameter families, generic modules and tameness -- 0.3. Canonical algebras and exceptional curves -- 0.4. Tubular shifts -- 0.5. Tame bimodules and homogeneous exceptional curves -- 0.6. Rational points -- Part 1. The homogeneous case -- Chapter 1. Graded factoriality -- 1.1. Efficient automorphisms -- 1.2. Prime ideals and universal extensions -- 1.3. Prime ideals as annihilators -- 1.4. Noetherianness -- 1.5. Prime ideals of height one are principal -- 1.6. Unique factorization -- 1.7. Examples of graded factorial domains -- The non-simple bimodule case -- The quaternion case -- The square roots case -- Chapter 2. Global and local structure of the sheaf category -- 2.1. Serre's theorem -- 2.2. Localization at prime ideals -- 2.3. Noncommutativity and the multiplicities -- 2.4. Localizing with respect to the powers of a prime element -- 2.5. Zariski topology and sheafification -- Chapter 3. Tubular shifts and prime elements -- 3.1. Central prime elements -- 3.2. Non-central prime elements and ghosts -- Chapter 4. Commutativity and multiplicity freeness -- 4.1. Finiteness over the centre -- 4.2. Commutativity of the coordinate algebra -- 4.3. Commutativity of the function field -- Chapter 5. Automorphism groups -- 5.1. The automorphism group of a homogeneous curve -- 5.2. The structure of Aut(H) -- 5.3. The twisted polynomial case -- 5.4. On the Auslander-Reiten translation as functor -- 5.5. The quaternion case -- 5.6. The homogeneous curves over the real numbers -- 5.7. Homogeneous curves with finite automorphism group -- Part 2. The weighted case -- Chapter 6. Insertion of weights -- 6.1. p-cycles -- 6.2. Insertion of weights into central primes -- 6.3. Automorphism groups for weighted curves -- Chapter 7. Exceptional objects.

7.1. Transitivity of the braid group action -- 7.2. Exceptional objects and graded factoriality -- Chapter 8. Tubular exceptional curves -- 8.1. Slope categories and the rational helix -- 8.2. The index of a tubular exceptional curve -- 8.3. A tubular curve of index three -- 8.4. A related tubular curve of index two -- 8.5. Line bundles which are not exceptional -- Appendix A. Automorphism groups over the real numbers -- A.1. Tables for the domestic and tubular cases -- Appendix B. The tubular symbols -- Bibliography -- Index -- A -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- O -- P -- Q -- R -- S -- T -- U.

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