Journal of Algebraic Geometry Journal of Algebraic Geometry

     

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

Author(s): So Okada
Journal: J. Algebraic Geom. 15 (2006), 487-505.
Posted: March 9, 2006
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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:

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.
A. Bondal, D. Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences, Compositio Math. 125 (2001), no. 3, 327-344. MR 1818984 (2001m:18014)

4.
T. Bridgeland, Stability conditions on triangulated categories, math.AG/0212237.

5.
T. Bridgeland, Stability conditions on K3 surfaces, math.AG/0307164.

6.
S. Gelfand and Y. Manin, Methods of homological algebra, Second edition, Springer Monographs in Mathematics. Springer-Verlag, Berlin, (2003). MR 1950475 (2003m:18001)

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.
M. Douglas, D-branes on Calabi-Yau manifolds, European Congress of Mathematics, Vol. II (Barcelona, 2000), 449-466, Progr. Math, 202, Birkhäuser, Basel, (2001), also math.AG/0009209. MR 1909947 (2004d:81090)

9.
M. Douglas, D-branes, categories and $ \mathcal{N}=1$ supersymmetry, J. Math. Phys. 42 (2001), no. 7, 2818-2843, also hep-th/0011017. MR 1840318 (2003b:81158)

10.
M. Douglas, Dirichlet branes, homological mirror symmetry, and stability, Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002), 395-408, Higer Ed. Press, Beijing, (2002), also math. AG/0207021. MR 1957548 (2004c:81200)

11.
A. Gorodentsev, S. Kuleshov and A. Rudakov, $ t$-stabilities and $ t$-structures on triangulated categories. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 68 (2004), no. 4, 117-150, also math.AG/0312442 (English version). MR 2084563 (2005j:18008)


Additional Information:

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

PII: S 1056-3911(06)00432-2
Received by editor(s): January 11, 2005
Received by editor(s) in revised form: August 28, 2005
Posted: March 9, 2006

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