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
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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 $\operatorname {Stab}(\operatorname {D}(\mathbb {P}^{1}))$.
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BON 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.
BON1 A. Bondal, D. Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences, Compositio Math. 125 (2001), no. 3, 327–344.
BRD T. Bridgeland, Stability conditions on triangulated categories, math.AG/0212237.
BRD1 T. Bridgeland, Stability conditions on K3 surfaces, math.AG/0307164.
GM S. Gelfand and Y. Manin, Methods of homological algebra, Second edition, Springer Monographs in Mathematics. Springer-Verlag, Berlin, (2003).
COH H. Cohn, Conformal mapping on Riemann surfaces, Reprint of the 1967 edition, Dover Books on Advanced Mathematics Dover Publications, Inc., New York, 1980.
DOG1 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.
DOG2 M. Douglas, D-branes, categories and $\mathcal {N}=1$ supersymmetry, J. Math. Phys. 42 (2001), no. 7, 2818–2843, also hep-th/0011017.
DOG3 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.
GKR 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).
Additional Information
So Okada
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-9305
Email:
okada@math.umass.edu
Received by editor(s):
January 11, 2005
Received by editor(s) in revised form:
August 28, 2005
Published electronically:
March 9, 2006
