Quot Functors for Deligne-Mumford Stacks

By Martin Olsson, J. Starr. 2002

129 citations recorded by the source corpus.

Abstract Given a separated and locally finitely-presented Deligne-Mumford stack 𝒳 over an algebraic space S, and a locally finitely-presented 𝒪𝒳-module ℱ, we prove that the Quot functor Quot(ℱ/𝒳/S) is represented by a separated and locally finitely-presented algebraic space over S. Under additional hypotheses, we prove that the connected components of Quot(ℱ/𝒳/S) are quasi-projective over S. Dedicated to Steven L. Kleiman on the occasion of his 60th birthday.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ec64fe384bed113fa4a05cfe57260f4da7f763d4

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Local Systems on Proper Algebraic V -manifolds (2010, background): “See also Kresch-Vistoli [62], Olsson, and Starr [83], [81] for statements about existence of coverings.”
Period and index in the Brauer group of an arithmetic surface (2007, methodology): “The last statement is not found any of the references; it follows from the Grothendieck existence theorem for stacks [31] applied to the results of Section 2.”
On the geometry of Deligne-Mumford stacks (2009, background): “5.5], a generating sheaf exists forX if and only ifX is a quotient stack. Another result [ OS , Thm.”
QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, background): “Olsson-Starr [37], if X is a scheme projective”
Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, methodology): “) are embedded in the appropriate weighted projective stacks, denoted P(ρ) below. 1.5. Moduli of stacks: this paper. In section 2 we consider weighted projective stacks and their substacks. Following [OS03] substacks are parametrized by a Hilbert scheme. All substacks of P(ρ) are cyclotomic, in part”
On proper coverings of Artin stacks (2005, background): “1), and for separated Deligne–Mumford stacks by Olsson and Starr ([9], 2.”
Weighted Projective Embeddings, Stability of Orbifolds, and Constant Scarla Curvature Kär Metrics (2009, background): “ity of varieties.) By Proposition 2.11 we can now mimic this for polarised orbifolds, rst embedding in a weighted projective space P. The Hilbert scheme of suborbischemes of P has been constructed in [OS]. Therefore we are left with the problem of quotienting this by the action of Aut(P). At rst sig”
Remarks on the stack of coherent algebras (2006, background): “rom a proper Artin stack of ﬁnite presentation to a global quotient by a ﬂat linear algebraic group scheme. This gives generalizations of various recent results of Starr and Olsson contained in [10], [12], and [14]. In fact, 2.3.4 gives a natural complement to Theorem 1.1 of [10] for target stacks w”