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arXiv · 2108.09949

One numerical obstruction for rational maps between hypersurfaces

Ilya Karzhemanov
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Abstract

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

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Ilya Karzhemanov. 2023-11-13. One numerical obstruction for rational maps between hypersurfaces. https://arxiv.org/abs/2108.09949

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