NCTS Algebraic Geometry Learning Seminar will focus on the deformation theory in the first half year. This is the 6th talk of Part II.

Part II - Deformation of rational curves. The outline of the talks is based of Debarre’s book, [Deb01], with possible references to Kollar's book, [Kol96]. The talks will focus around chapters 3-5 of [Deb01], culminating in proving an effective bound for the volume of a smooth Fano variety based on dimensions which implies the boundedness of family of smooth Fano varieties.

 

Talk 7 (Structure of MRC)  In this talk we will explain the result in [GHS03], which is used to prove that the base of the MRC fibration is not uniruled.

 

[GHS03] Tom Graber, Joe Harris, and Jason Starr. Families of rationally connected varieties. J. Amer. Math. Soc., 16(1):57–67, 2003.

 

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

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