Remarks on the stack of coherent algebras

By Max Lieblich. International mathematics research notices, 2006

78 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0dfc59b75189648b787a9a0bad892911e69daef9

How researchers see this paper

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In Algebra and Number Theory

1. Bumsig Kim
2. Ionut Ciocan-Fontanine
3. Xuhua He
4. Davesh Maulik

In Computational Theory and Mathematics

1. Bumsig Kim
2. Ionut Ciocan-Fontanine
3. Davesh Maulik
4. Michael Rapoport
5. S. Nie

In Geometry and Topology

1. Bumsig Kim
2. Ionut Ciocan-Fontanine
3. Daewoong Cheong
4. Davesh Maulik
5. J. Starr
6. A. J. Jong
7. Xuhua He
8. D. Huybrechts

Citations in the corpus

• Families of rationally simply connected varieties over surfaces and torsors for semisimple groups (2008, background): “Proposition 2.6. See [ Lie06 , Proposition 2.11].”
• Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks (2008, unknown): “ford stack is algebraic and we provide it with an explicit smooth atlas . The algebraicity of the stack is an already known result and it is stated in more generality (no projectivity is required) in [Lie06]; however, we have decided to include this proof since it is elementary explicit and it is al”
• Orbifold quasimap theory (2014, background): “11 in [25] since S is an excellent scheme over C and X × S is the quotient stack [W ×S/G].”
• Stable quasimaps to GIT quotients (2011, background): “While the fact that Qmapg,k(W/G, β) is an Artin stack locally of finite type follows quite easily by combining some results in [32] and [1], we give a straightforward direct construction which exhibits it as a stack with a schematic morphism toBunG, whose fibers”