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arXiv · 2012.11194

Moduli of Admissible Pairs for Arbitrary Dimension, I: Resolution

Nadezhda V. Timofeeva
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Abstract

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.

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Nadezhda V. Timofeeva. 2020-12-21. Moduli of Admissible Pairs for Arbitrary Dimension, I: Resolution. https://arxiv.org/abs/2012.11194

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