English

Moduli of Admissible Pairs for Arbitrary Dimension, I: Resolution

Algebraic Geometry 2025-09-30 v4

Abstract

A procedure resolving a torsion-free coherent sheaf on a nonsingular NN-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.

Keywords

Cite

@article{arxiv.2012.11194,
  title  = {Moduli of Admissible Pairs for Arbitrary Dimension, I: Resolution},
  author = {Nadezhda V. Timofeeva},
  journal= {arXiv preprint arXiv:2012.11194},
  year   = {2025}
}

Comments

22 p. There was a mistake in the previous version (in the proof of flatness of the family obtained). All concerning this point was removed