Some moduli spaces for rank $2$ stable reflexive sheaves on $\textbf {P}^ 3$
HTML articles powered by AMS MathViewer
- by Rosa M. Miró-Roig PDF
- Trans. Amer. Math. Soc. 299 (1987), 699-717 Request permission
Abstract:
In [Ma], Maruyama proved that the set $M({c_1},{c_2},{c_3})$ of isomorphism classes of rank $2$ stable reflexive sheaves on ${{\mathbf {P}}^3}$ with Chern classes $({c_1},{c_2},{c_3})$ has a natural structure as an algebraic scheme. Until now, there are no general results about these schemes concerning dimension, irreducibility, rationality, etc. and only in a few cases a precise description of them is known. This paper is devoted to the following cases: (i) $M( - 1,{c_2},c_2^2 - 2r{c_2} + 2r(r + 1))$ with ${c_2} \geqslant 4$, $1 \leqslant r \leqslant ( - 1 + \sqrt {4{c_2} - 7} )/2$; and (ii) $M( - 1,{c_2},c_2^2 - 2(r - 1){c_2})$ with ${c_2} \geqslant 8$, $2 \leqslant r \leqslant ( - 1 + \sqrt {4{c_2} - 7} )/2$.References
- Mei Chu Chang, Stable rank $2$ reflexive sheaves on $\textbf {P}^{3}$ with large $c_{3}$, J. Reine Angew. Math. 343 (1983), 99–107. MR 705879, DOI 10.1515/crll.1983.343.99
- Mei-Chu Chang, Stable rank $2$ reflexive sheaves on $\textbf {P}^{3}$ with small $c_{2}$ and applications, Trans. Amer. Math. Soc. 284 (1984), no. 1, 57–89. MR 742412, DOI 10.1090/S0002-9947-1984-0742412-8
- Robin Hartshorne, Stable reflexive sheaves, Math. Ann. 254 (1980), no. 2, 121–176. MR 597077, DOI 10.1007/BF01467074
- Robin Hartshorne, Stable reflexive sheaves. II, Invent. Math. 66 (1982), no. 1, 165–190. MR 652652, DOI 10.1007/BF01404762
- Robin Hartshorne, Residues and duality, Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin-New York, 1966. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64; With an appendix by P. Deligne. MR 0222093, DOI 10.1007/BFb0080482
- Masaki Maruyama, Moduli of stable sheaves. II, J. Math. Kyoto Univ. 18 (1978), no. 3, 557–614. MR 509499, DOI 10.1215/kjm/1250522511 R. M. Miró, The moduli space ${M_{{{\mathbf {P}}^3}}}( - 1,{c_2},c_2^2 - 2{c_2} + 4)$, preprint 1983.
- Rosa M. Miró-Roig, Gaps in Chern classes of rank $2$ stable reflexive sheaves, Math. Ann. 270 (1985), no. 3, 317–323. MR 774359, DOI 10.1007/BF01473429
- Christian Okonek, Moduli extremer reflexiver Garben auf $\textbf {P}^{n}$, J. Reine Angew. Math. 338 (1983), 183–194 (German). MR 684022, DOI 10.1515/crll.1983.338.183 T. Sauer, Nonstable reflexive sheaves on ${{\mathbf {P}}^3}$, preprint.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 299 (1987), 699-717
- MSC: Primary 14F05; Secondary 14D20
- DOI: https://doi.org/10.1090/S0002-9947-1987-0869229-0
- MathSciNet review: 869229