Moduli of Admissible Pairs for Arbitrary Dimension, I: Resolution
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866916973487587328 |
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| author | Timofeeva, Nadezhda V. |
| author_facet | Timofeeva, Nadezhda V. |
| contents | A procedure resolving a torsion-free coherent sheaf on a nonsingular $N$-dimensional projective algebraic variety into a locally free sheaf on a projective scheme of certain class is proposed. This is a higher-dimensional analog of the resolution (called the standard resolution in previous works of the author) of coherent sheaves on a surface. The method is applicable to all existing flat families of torsion-free sheaves including those who does not contain locally free sheaves.
Bibliography: 23 items
Keywords: moduli space, algebraic coherent sheaves, admissible pairs, vector bundles, nonsingular algebraic variety, projective algebraic variety, moduli of vector bundles, compactification of moduli. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_11194 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Moduli of Admissible Pairs for Arbitrary Dimension, I: Resolution Timofeeva, Nadezhda V. Algebraic Geometry 14F06, 14D20, 14D06 A procedure resolving a torsion-free coherent sheaf on a nonsingular $N$-dimensional projective algebraic variety into a locally free sheaf on a projective scheme of certain class is proposed. This is a higher-dimensional analog of the resolution (called the standard resolution in previous works of the author) of coherent sheaves on a surface. The method is applicable to all existing flat families of torsion-free sheaves including those who does not contain locally free sheaves. Bibliography: 23 items Keywords: moduli space, algebraic coherent sheaves, admissible pairs, vector bundles, nonsingular algebraic variety, projective algebraic variety, moduli of vector bundles, compactification of moduli. |
| title | Moduli of Admissible Pairs for Arbitrary Dimension, I: Resolution |
| topic | Algebraic Geometry 14F06, 14D20, 14D06 |
| url | https://arxiv.org/abs/2012.11194 |