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Non-commutative thickening of moduli spaces of stable sheaves

Part of: Algebraic geometry: Foundations Families, fibrations

Published online by Cambridge University Press:  26 April 2017

Yukinobu Toda
Yukinobu Toda*
Affiliation:
Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan email yukinobu.toda@ipmu.jp
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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.

Keywords

non-commutative deformationsmoduli spaces of stable sheaves

MSC classification

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles
Secondary: 14A22: Noncommutative algebraic geometry

Information

Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 6 , June 2017 , pp. 1153 - 1195
Copyright
© The Author 2017 

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