Zahme abgeleitete Kategorien und ihre Anwendungen in der Algebraischen Geometrie, Darstellungstheorie, Singularitätentheorie und der mathematischen Physik

• Applicant: Professor Dr. Igor Burban
• Subject Area: Mathematics
• Term: from 2007 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 43209539

• Final Report Year: 2014

Final Report Abstract

No abstract available

Publications

• Maximal Cohen–Macaulay modules over surface singularities, Trends in Representations of Algebras and Related Topics, 101–160, EMS Publishing House (2008)
  I. Burban, Yu. Drozd
  
• Mutation–classes of diagrams via infinite graphs, Math. Nachr. 284 (2011), no. 17-18, 2184–2205
  T. Henrich
  
• Tilting on non-commutative rational projective curves, Mathematische Annalen 351, no. 3, 665–709 (2011)
  I. Burban, Yu. Drozd
  
• Frobenius morphism and vector bundles on cycles of projective lines, Comm. in Algebra 40, no. 8, 2983–2988 (2012)
  I. Burban
  (See online at https://doi.org/10.1080/00927872.2011.588633)
• On the Hall algebra of an elliptic curve I, Duke Math. Journal, vol. 161, no. 7, 1171–1231 (2012)
  I. Burban, O. Schiffmann
  
• Semi-stable vector bundles on elliptic curves and the associative Yang–Baxter equation, Journal of Geometry and Physics 62, no. 2, 312–329 (2012)
  I. Burban, T. Henrich
  (See online at https://doi.org/10.1016/j.geomphys.2011.11.001)
• Singularity category of a non-commutative resolution of singularities, Adv. in Math., vol. 231, no. 1, 414–435 (2012)
  I. Burban, M. Kalck
  
• Two descriptions of the quantum affine algebra Uv (sl2 ) via Hall algebra approach, Glasgow Journal of Math. 54, no.2, 283–307 (2012)
  I. Burban, O. Schiffmann
  
• Vector bundles on degenerations of elliptic curves and Yang–Baxter equations, Memoirs of the AMS 220, no. 1035 (2012)
  I. Burban, B. Kreußler
  
• Vector bundles on plane cubic curves and the classical Yang-Baxter equation, Journal of the European Math. Soc.
  I. Burban, T. Henrich
  
• Composition algebra of a weighted projective line, J. Reine Angew. Math, vol. 679, 75–124 (2013)
  I. Burban, O. Schiffmann
  
• Analytic moduli spaces of simple sheaves on families of integral curves, Math. Nachr., vol. 287, no. 2-3, 173–183 (2014)
  I. Burban, B. Kreußler
  (See online at https://doi.org/10.1002/mana.201200355)