Non-commutative thickening of moduli spaces of stable sheaves

Abstract

We show that the moduli spaces of stable sheaves on projective schemes admit certain non-commutative structures, which we call quasi NC structures, generalizing Kapranov's NC structures. The completion of our quasi NC structure at a closed point of the moduli space gives a pro-representable hull of the non-commutative deformation functor of the corresponding sheaf developed by Laudal, Eriksen, Segal and Efimov-Lunts-Orlov. We also show that the framed stable moduli spaces of sheaves have canonical NC structures.

42 pages

References in corpus (2)

• A 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications
• A functorial construction of moduli of sheaves

Cited by in corpus (2)

• Formality conjecture for K3 surfaces
• NC-smooth algebroid thickenings for families of vector bundles and quiver representations