## On the number of rational maps between varieties of general type

J. Math. Sci. Univ. Tokyo
Vol. 1 (1994), No. 2, Page 423--433.

Bandman, T. ; Markushevich, D.
On the number of rational maps between varieties of general type
Let $X,Y$ be two complex projective varieties with only canonical singularities and big and nef canonical line bundles $K_X , K_Y$. Then the set $R(X,Y)$ of all dominant rational maps $f : X \to Y$ is finite. We prove that the number $\# R(X,Y)$ of this maps has the upper estimate, which depends only on the dimension $dim X=n$, selfintersection $K^n_X$ and product $r=r_Xr_Y$ of indices $r_X$ and $r_Y$ of varieties $X$ and $Y$.