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 2 (Chapter II, Sec. 6-9) Obstructions for higher- order deformations of line bundles, subvarieties, coherent sheaves. Deforma- tion of singular schemes.

 

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. To be announced later.