Non-commutative thickening of moduli spaces of stable sheaves

作者：Toda Yukinobu^*

来源：Compositio Mathematica, 2017, 153(6): 1153-1195.

DOI：10.1112/S0010437X17007047

• non-commutative deformations
• moduli spaces of stable sheaves

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.

• 出版日期2017-6