Kyungyong Lee

Introduction to Cremona Transformations


For a birational (Cremona) map P^n ----> P^n, consider the graph T in P^n x P^n.  Then T is an n-dimensional integral subscheme whose rational equivalence class is a linear combination of [P^n x pt], [P^{n-1} x P^1], ... , [pt x P^n].  We can naturally ask which rational equivalence classes can occur.  The answers are known only for n=2,3.  It is known that the coefficients should satisfy Hodge index type inequalities.  I'll introduce various aspects of Cremona transformations, focusing on concrete examples.