One numerical obstruction for rational maps between hypersurfaces

Ilya Karzhemanov

Published 2021-08-23Version 1

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