Toward a definition of moduli of complexes of coherent sheaves on a projective scheme

By M. Inaba. 2002

96 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b6506b9c872d1f8a2a6b3d52ec65a728fff88edf

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Stability Conditions on An-Singularities (2010, methodology): “Since we have Ext1Xk′ (Ek′ , Ek′) = 0 and Ext0Xk′ (Ek′ , Ek′) ∼= k ′, the deformation theory in [29] implies that E and F are isomorphic on some étale covering of SpecR.”
Moduli of objects in dg-categories (2005, background): “5 (2)), recover and provide new proofs of the result of the recent paper [19] (and thus of [11]), at least in the smooth case.”
Stability conditions on Kuznetsov components (2017, unknown): “We denote by M spl(Ku(X)) the space parameterizing simple objects in Ku(X), which is an algebraic space locally of finite-type over C by [Ina02].”
Moduli of complexes on a proper morphism (2005, background): “The deformation theory of complexes can be made quite explicit when working on a flat projective morphism, as in [14].”
A categorical invariant for cubic threefolds (2009, background): “For a cubic threefold Y , following [19, 20], define a functor”
Derived categories of coherent sheaves (2006, result): “Recent results of Inaba [22] and Toen and Vaquie [49] construct spaces parameterising very general classes of objects of derived categories.”
Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes (2008, background): “In [12] (see also [8]) it was shown under very general assumptions that complexes as objects in the derived category form an Artin stack which is locally of finite type.”
Moduli stacks and invariants of semistable objects on K3 surfaces (2007, background): “Hence by Inaba’s work [14] and the openness of stability proved in Section 4, there is an algebraic space M̃ (α,φ)(σ) which parameterizes the objects in M (α,φ)(σ).”
Projectivity and birational geometry of Bridgeland moduli spaces on an Enriques surface (2014, background): “Inaba proved in [20] that Mσ,Y (v) is a Gm-gerbe over a separated algebraic space that we denote by M σ,Y (v).”