Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Stability manifold of $ \mathbb{P}^{1}$


Author: So Okada
Journal: J. Algebraic Geom. 15 (2006), 487-505
DOI: https://doi.org/10.1090/S1056-3911-06-00432-2
Published electronically: March 9, 2006
MathSciNet review: 2219846
Full-text PDF

Abstract | References | Additional Information

Abstract: We describe the stability manifold of the bounded derived category $ \operatorname{D}(\mathbb{P}^{1})$ of coherent sheaves on $ \mathbb{P}^{1}$, denoted $ \operatorname{Stab}(\operatorname{D}(\mathbb{P}^{1}))$.


References [Enhancements On Off] (What's this?)

  • 1. A. Be{\u{\i\/}}\kern.15emlinson, Coherent Sheaves on $ {\mathbb{P}}^n$ and Problems in Linear Algebra, (Russian) Funktsional. Anal. i Prilozhen. 12 (1978), no. 3, 68-69, also English translation: Functional Anal. Appl. 12 (1978), no. 3, 212-214 (1979); ibid. 12 (1978), no. 3, 214-216 (1979). MR 0509388 (80c:14010b)
  • 2. A. Bondal, Representations of associative algebras and coherent sheaves, (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), no. 1, 25-44, also English translation in Math. USSR-Izv. 34 (1990), no. 1, 23-42. MR 0992977 (90i:14017)
  • 3. Alexei Bondal and Dmitri Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences, Compositio Math. 125 (2001), no. 3, 327–344. MR 1818984, https://doi.org/10.1023/A:1002470302976
  • 4. T. Bridgeland, Stability conditions on triangulated categories, math.AG/0212237.
  • 5. T. Bridgeland, Stability conditions on K3 surfaces, math.AG/0307164.
  • 6. Sergei I. Gelfand and Yuri I. Manin, Methods of homological algebra, 2nd ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003. MR 1950475
  • 7. H. Cohn, Conformal mapping on Riemann surfaces, Reprint of the 1967 edition, Dover Books on Advanced Mathematics Dover Publications, Inc., New York, 1980. MR 0594937 (82a:30009)
  • 8. Michael R. Douglas, D-branes on Calabi-Yau manifolds, European Congress of Mathematics, Vol. II (Barcelona, 2000) Progr. Math., vol. 202, Birkhäuser, Basel, 2001, pp. 449–466. MR 1909947
  • 9. Michael R. Douglas, D-branes, categories and 𝒩=1 supersymmetry, J. Math. Phys. 42 (2001), no. 7, 2818–2843. Strings, branes, and M-theory. MR 1840318, https://doi.org/10.1063/1.1374448
  • 10. Michael R. Douglas, Dirichlet branes, homological mirror symmetry, and stability, Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002) Higher Ed. Press, Beijing, 2002, pp. 395–408. MR 1957548
  • 11. A. L. Gorodentsev, S. A. Kuleshov, and A. N. Rudakov, 𝑡-stabilities and 𝑡-structures on triangulated categories, Izv. Ross. Akad. Nauk Ser. Mat. 68 (2004), no. 4, 117–150 (Russian, with Russian summary); English transl., Izv. Math. 68 (2004), no. 4, 749–781. MR 2084563, https://doi.org/10.1070/IM2004v068n04ABEH000497


Additional Information

So Okada
Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-9305
Email: okada@math.umass.edu

DOI: https://doi.org/10.1090/S1056-3911-06-00432-2
Received by editor(s): January 11, 2005
Received by editor(s) in revised form: August 28, 2005
Published electronically: March 9, 2006

American Mathematical Society