NCTS Algebraic Geometry Learning Seminar will focus on the deformation theory in the first half year. This is 1st 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 1 (Bend-Break Lemma) Covers Chapter 3 (with possible reference to chapter 2). 

 

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.