The moduli stack of stable relative ideal sheaves
arXiv:math/0701074
Abstract
In this paper, we propose a definition of the moduli stack of stable relative ideal sheaves, and prove that it is a separated and proper Deligne-Mumford stack. It is the first part of the project of relative Donaldson-Thomas theory of ideal sheaves on projective threefolds, which in the end provides a degeneration formula of Donaldson-Thomas invariants of threefolds.
This paper has been withdrawn. More general results have been proved for Quot-schemes in the paper see arxiv:1110.0390 "Good degeneration of Quot-schemes and coherent systems" joint with Jun Li