ncku-talk2011-12-02

NCTS(South)/ NCKU Math Colloquium

DATE 2011-12-02　16:10-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Chen, Jung-Kai( 陳榮凱)（臺灣大學數學系）

TITLE Factoring birational maps in dimesnion three.

ABSTRACT Birational maps in minimal model program consist of the following elementary ones:� divisorial contractions, flips and flops. Divisorial contractions are the higher dimensional analog of the inverse of blowing up a smooth point on a surface. A flips (resp. flop) is an operation which consists of a ``surgery'' in codimension $\geq 2$ which replaces certain $K_X$-negative (resp. $K_X$-trivial) curves by some $K_X$-positive (resp. $K_X$-trivial) curves.
Starting with a non-minimal projective variety, then one expects to obtain a minimal model of $X$ by a finite sequence of flips and divisorial contractions.In dimension three, many of these birational maps admit explicit description. We survey some recent advances in explicit studies of birational maps in minimal model program in dimension three.

NCTS(South)/ NCKU Math Colloquium

DATE	2011-12-02　16:10-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Chen, Jung-Kai( 陳榮凱)（臺灣大學數學系）

TITLE	Factoring birational maps in dimesnion three.

ABSTRACT	Birational maps in minimal model program consist of the following elementary ones:� divisorial contractions, flips and flops. Divisorial contractions are the higher dimensional analog of the inverse of blowing up a smooth point on a surface. A flips (resp. flop) is an operation which consists of a ``surgery'' in codimension $\geq 2$ which replaces certain $K_X$-negative (resp. $K_X$-trivial) curves by some $K_X$-positive (resp. $K_X$-trivial) curves. Starting with a non-minimal projective variety, then one expects to obtain a minimal model of $X$ by a finite sequence of flips and divisorial contractions.In dimension three, many of these birational maps admit explicit description. We survey some recent advances in explicit studies of birational maps in minimal model program in dimension three.