Hecke correspondences for smooth moduli spaces of sheaves
Andrei Neguţ
Abstract
We define functors on the derived category of the moduli space ℳ of stable sheaves on a smooth projective surface (under Assumptions A and S below), and prove that these functors satisfy certain commutation relations. These relations allow us to prove that the given functors induce an action of the elliptic Hall algebra on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> </mml:math> -theory of the moduli space ℳ, thus generalizing the action studied by Nakajima, Grojnowski and Baranovsky in cohomology.
Topics & Concepts
Moduli spaceFunctorMathematicsPure mathematicsAction (physics)CohomologyModuliSpace (punctuation)Algebra over a fieldComputer sciencePhysicsOperating systemQuantum mechanicsAlgebraic structures and combinatorial modelsAlgebraic Geometry and Number TheoryAdvanced Algebra and Geometry