ncku-talk2019-11-07

Colloquium

DATE 2019-11-07　15:10-16:00

PLACE 數學館3174教室

SPEAKER 川又雄二郎 (Yujiro Kawamata ) 教授（ University of Tokyo/KAIST/NCTS）

TITLE Non-commutative Deformations of Coherent Sheaves

ABSTRACT We consider deformations of a coherent sheaf on an algebraic variety.The deformations are usually considered over commutative rings, and the parameter ring of the universal deformation is the local ring of the moduli space of the sheaf.When we allow non-commutativity of the parameter ring, then we obtain similar theory but with more deformations.For example, if we consider the structure sheaf of a line in a projective space, the moduli space of the usual deformations is the Grassmann variety.But there are more non-commutative deformations than the commutative ones, and they are obstructed.We will explain how to describe the universal non-commutative deformations.

Colloquium

DATE	2019-11-07　15:10-16:00

PLACE	數學館3174教室

SPEAKER	川又雄二郎 (Yujiro Kawamata ) 教授（ University of Tokyo/KAIST/NCTS）

TITLE	Non-commutative Deformations of Coherent Sheaves

ABSTRACT	We consider deformations of a coherent sheaf on an algebraic variety.The deformations are usually considered over commutative rings, and the parameter ring of the universal deformation is the local ring of the moduli space of the sheaf.When we allow non-commutativity of the parameter ring, then we obtain similar theory but with more deformations.For example, if we consider the structure sheaf of a line in a projective space, the moduli space of the usual deformations is the Grassmann variety.But there are more non-commutative deformations than the commutative ones, and they are obstructed.We will explain how to describe the universal non-commutative deformations.