Hecke correspondences for smooth moduli spaces of sheaves

2018/04/10 by Neguţ, Andrei · 2 citations
#14D20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1804.03645

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 relations. These relations allow us to prove that the given functors induce an action of the elliptic Hall algebra on the K-theory of the moduli space M, thus generalizing the action studied by Nakajima, Grojnowski and Baranovsky in cohomology.

Cited by

• Instantons on the Blown-up Surface and the Affine Vertex Algebra
• Abel maps for integral curves via a derived perspective

Related

• Shuffle algebras associated to surfaces
• Moduli of Sheaves on Surfaces and Action of the Oscillator Algebra
• Rational, trigonometric, elliptic algebras and moduli spaces of sheaves on surfaces
• K-theory of moduli spaces of sheaves and large Grassmannians
• The cohomological Hall algebra of a surface and factorization cohomology