72
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Blowing-Ups Describing the Polarization Change of Moduli Schemes of Semistable Sheaves of General Rank

Pages 3094-3110 | Received 01 Mar 2007, Published online: 18 Aug 2010

REFERENCES

  • Ellingsrud , G. , Göttsche , L. ( 1995 ). Variation of moduli spaces and Donaldson invariants under change of polarization . J. Reine Angew. Math. 467 : 1 – 49 .
  • Friedman , R. Vector bundles and so(3)-invariants for elliptic surfaces . J. Amer. Math. Soc. 8 .
  • Friedman , R. , Qin , Z. ( 1995 ). Flips of moduli spaces and transition formulas for Donaldson polynomial invariants of rational surfaces . Comm. Anal. Geom. 3 ( 1–2 ): 11 – 83 .
  • Gieseker , D. ( 1977 ). On the moduli of vector bundles on an algebraic surface . Ann. Math. (2) 106 ( 1 ): 45 – 60 .
  • Hartshorne , R. ( 1966 ). Residues and Duality . Lecture Notes in Mathematics, Vol. 20 . Berlin : Springer-Verlag .
  • He , M. ( 1998 ). Espaces de modules de systèmes cohérents . Internat. J. Math. 9 ( 5 ): 545 – 598 .
  • Huybrechts , D. , Lehn , M. ( 1997 ). The Geometry of Moduli Spaces of Sheaves . Friedr. Vieweg & Sohn .
  • Laudal , A. ( 1986 ). Matric Massey Products and Formal Moduli i, Algebra, Algebraic Topology and Their Interactions . Lecture Notes in Mathematics, Vol. 1183 . Springer Verlag , pp. 218 – 240 .
  • Maruyama , M. ( 1978 ). Moduli of stable sheaves, II . J. Math. Kyoto Univ. 18 ( 3 ): 557 – 614 .
  • Maruyama , M. ( 1982 ). Elementary transformations in the theory of algebraic vector bundles. Algebraic Geometry (La Rábida, 1981), Berlin: Springer, pp. 241–266 .
  • Maruyama , M. , Yokogawa , K. (1992). Moduli of parabolic stable sheaves. Math. Ann. 293(1):77–99.
  • Matsuki , K. , Wentworth , R. ( 1997 ). Mumford–Thaddeus principle on the moduli space of vector bundles on an algebraic surface . Internat. J. Math. 8 ( 1 ): 97 – 148 .
  • Matsumura , M. ( 1986 ). Commutative Ring Theory . Cambridge Univ. Press .
  • Mochizuki , T. ( 2009 ). Donaldson Type Invariants for Algebraic Surface . Lecture Notes in Mathematics, Vol. 1972 . Berlin : Springer-Verlag .
  • Mukai , S. ( 1984 ). Symplectic structure of the moduli space of sheaves on an abelian or K3 surface . Invent. Math. 77 ( 1 ): 101 – 116 .
  • O'Grady , K. G. ( 1996 ). Moduli of vector bundles on projective surfaces: some basic results . Invent. Math. 123 ( 1 ): 141 – 207 .
  • Simpson , C. T. ( 1994 ). Moduli of representations of the fundamental group of a smooth projective variety. I . Inst. Hautes Études Sci. Publ. Math. ( 79 ): 47 – 129 .
  • Thaddeus , M. ( 1996 ). Geometric invariant theory and flips . J. Amer. Math. Soc. 9 ( 3 ): 691 – 723 .
  • Tyurin , A. N. ( 1988 ). Symplectic structures on the moduli spaces of vector bundles on algebraic surfaces with p g  > 0 . Izv. Akad. Nauk SSSR Ser. Mat. 52 ( 4 ): 813 – 852 , 896 .
  • Yamada , K. ( 2003 ). A sequence of blowing-ups connecting moduli of sheaves and the Donaldson polynomial under change of polarization . J. Math. Kyoto Univ. 43 ( 4 ): 829 – 878 . math.AG/0704.2866 .
  • Yoshioka , K. ( 1996 ). Chamber structure of polarizations and the moduli of stable sheaves on a ruled surface . Internat. J. Math. 7 ( 3 ): 411 – 431 .
  • Communicated by L. Ein.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.