Quiver Grassmannians of Extended Dynkin Type d Part I

Let Q be a quiver of extended Dynkin type \widetilde{D}_n. In this first of two papers, the authors show that the quiver Grassmannian \mathrm{Gr}_{underline{e}}(M) has a decomposition into affine spaces for every dimension vector underline{e} and every indecomposable representation M of defect -1 an...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Lorscheid, Oliver
Otros Autores: Weist, Thorsten
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2019.
Colección:Memoirs of the American Mathematical Society Ser.
Temas:
Geometry, Algebraic.
Géométrie algébrique.
Geometría algebraica
Geometry, Algebraic
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title page
  • Introduction
  • Chapter 1. Background
  • 1.1. Coefficient quiver
  • 1.2. Schubert decompositions
  • 1.3. Representations of Schubert cells
  • Chapter 2. Schubert systems
  • 2.1. The complete Schubert system
  • 2.2. Partial Evaluations
  • 2.3. Contradictory -states
  • 2.4. Definition of -states
  • 2.5. The reduced Schubert system
  • 2.6. Computing -states
  • 2.7. Solvable -states
  • 2.8. Extremal edges
  • 2.9. Patchwork solutions
  • 2.10. Extremal paths
  • Chapter 3. First applications
  • 3.1. The Kronecker quiver
  • 3.2. Dynkin quivers
  • Chapter 4. Schubert decompositions for type ̃ _{ }
  • 4.1. Contradictory of the first and of the second kind
  • 4.2. Automorphisms of the Dynkin diagram
  • 4.3. Bases for some indecomposable representations
  • 4.4. The main theorem
  • Chapter 5. Proof of Theorem 4.1
  • 5.1. Defect -1
  • Appendix A. Representations for quivers of type ̃ _{ }
  • A.1. Reflections and Auslander-Reiten translates
  • A.2. Indecomposable and exceptional representations
  • A.3. The Auslander-Reiten quiver
  • A.4. The tubes
  • A.5. Roots
  • A.6. The defect
  • Appendix B. Bases for representations of type ̃ _{ }
  • B.1. Defect -1
  • B.2. Defect -2
  • B.3. Positive defect
  • B.4. Exceptional tubes of rank 2
  • B.5. Exceptional tubes of rank -2
  • B.6. Homogeneous tubes
  • Bibliography
  • Back Cover

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