Moduli of Admissible Pairs for Arbitrary Dimension, I: Resolution
arXiv:2012.11194
Abstract
A procedure resolving a torsion-free coherent sheaf on a nonsingular -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.
arXiv comment22 p. There was a mistake in the previous version (in the proof of flatness of the family obtained). All concerning this point was removed