One numerical obstruction for rational maps between hypersurfaces

Abstract

Given a rational dominant map $\varphi :Y⇢X$ between two generic hypersurfaces $Y,X\subset {\mathbb{P}}^n$ of dimension $\ge 3$, we prove (under an addition assumption on $\varphi$) a "Noether-Fano type" inequality $m_Y\ge m_X$ for certain (effectively computed) numerical invariants of $Y$ and $X$.

11 pages