English

Moduli of PT-semistable objects II

Algebraic Geometry 2011-05-05 v2 Mathematical Physics math.MP

Abstract

We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category Db(X)D^b(X) of coherent sheaves on a smooth projective three-fold XX. Then we construct the moduli of PT-semistable objects in Db(X)D^b(X) as an Artin stack of finite type that is universally closed. In the absence of strictly semistable objects, we construct the moduli as a proper algebraic space of finite type.

Keywords

Cite

@article{arxiv.1011.6306,
  title  = {Moduli of PT-semistable objects II},
  author = {Jason Lo},
  journal= {arXiv preprint arXiv:1011.6306},
  year   = {2011}
}

Comments

34 pages. Exposition improved based on referee's comments, especially the proofs of Prop 2.6 and 2.17 (of this version). References added; typos corrected. Openness and separatedness now in a separate section. Sections 4 and 5 of previous version removed. Accepted for publication by the Transactions of the American Mathematical Society. This is the sequel to http://arxiv.org/abs/1011.5688

R2 v1 2026-06-21T16:50:29.690Z