Some moduli spaces for rank 2 reflexive sheaves on $ {{\mathbf{P}}^3}$
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 conc...
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| Format: | article |
| Status: | Published version |
| Publication Date: | 1987 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/95817 |
| Online Access: | https://hdl.handle.net/2445/95817 |
| Access Level: | Open access |
| Keyword: | Geometria algebraica Homologia Algebraic geometry Homology |
| Summary: | 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$. |
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