NCTS Algebraic Geometry Learning Seminar will focus on the deformation theory in the first half year.

 

Part I - Abstract deformation theory. Reference: [Har10]. Pre-requisite: We should assume everyone is familiar with the definition and basic properties of the Hilbert scheme (but not with its construction). If this is not the case, we should recall them during the first talk.

 

Talk 1 (Chapter I) First order deformations of line bundles, subvarieties, coherent sheaves. Construction and properties of the functors. Infinitesimal lifting property, smoothness of a morphism and vanishing of >0. Deformation of rings via . Example: deformation of cones.

 

Part I - Abstract deformation theory. We mainly follow Hartshorne's Deformation Theory book.

Part II - Deformation theory and DGLA. We follow Manetti's note.

Part III - Deformation of rational curves. We follow Debarre's Higher Dimensional Algebraic Geometry.

Part IV - Other related work. Announced later.