Moduli of Admissible Pairs for Arbitrary Dimension, I: Resolution

Nadezhda V. Timofeeva

Published 2020-12-21Version 1

The procedure of resolution for a flat family of torsion-free coherent sheaves on a non-singular N-dimensional projective algebraic variety into the flat family of locally free sheaves on projective schemes of certain class is proposed. This is higher-dimensional analogue of standard resolution of coherent sheaves on a surface. The consideration is applicable to all families of torsion-free sheaves as they exist, including those containing no locally free sheaves.