Remarks on the stack of coherent algebras

Details Remarks on the stack of coherent algebras Remarks on the stack of coherent algebras

2006-03-02

arxiv.org/abs/math/0603034v2

Mathematics

Algebraic Geometry

9 pages; several sections and new results added; to appear in IMRN

Scientific paper

We consider the stack of coherent algebras with proper support, a moduli problem generalizing Alexeev and Knutson's stack of branchvarieties to the case of an Artin stack. The main results are proofs of the existence of Quot and Hom spaces in greater generality than is currently known and several applications to Alexeev and Knutson's original construction: a proof that the stack of branchvarieties is always algebraic, that limits of one-dimensional families always exist, and that the connected components of the stack of branchvarieties are proper over the base under certain hypotheses on the ambient stack.

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