Morphisms from a very general hypersurface
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2019
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909751716085760 |
|---|---|
| author | Lee, Yongnam Luo, Yujie Zhang, De-Qi |
| author_facet | Lee, Yongnam Luo, Yujie Zhang, De-Qi |
| contents | Let $X$ be a very general hypersurface of degree $d$ in the projective $(n+1)$-space with $n \ge 3$, and $f: X \to Y$ a non-birational surjective morphism to a normal projective variety $Y$. We first prove that $Y$ is a klt Fano variety if ${\rm deg} \, f \ge C$ for some constant $C = C(n, d)$ depending only on $n$ and $d$. Next we prove an optimal upper bound ${\rm deg} \, f \le {\rm deg} \, X$ provided that $Y$ is factorial, ${\rm deg} \, f$ is prime and ${\rm deg} \, f \ge E(n)$ for some constant $E(n)$ (with $E(n) = n(n+1)$ when $Y$ is smooth). As a corollary, we show that $Y\cong {\bf P}^n$ under some conditions on $Y$ and ${\rm deg} \, f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_06894 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Morphisms from a very general hypersurface Lee, Yongnam Luo, Yujie Zhang, De-Qi Algebraic Geometry 14E05, 14D05, 14J45, 14J70, 14M22 Let $X$ be a very general hypersurface of degree $d$ in the projective $(n+1)$-space with $n \ge 3$, and $f: X \to Y$ a non-birational surjective morphism to a normal projective variety $Y$. We first prove that $Y$ is a klt Fano variety if ${\rm deg} \, f \ge C$ for some constant $C = C(n, d)$ depending only on $n$ and $d$. Next we prove an optimal upper bound ${\rm deg} \, f \le {\rm deg} \, X$ provided that $Y$ is factorial, ${\rm deg} \, f$ is prime and ${\rm deg} \, f \ge E(n)$ for some constant $E(n)$ (with $E(n) = n(n+1)$ when $Y$ is smooth). As a corollary, we show that $Y\cong {\bf P}^n$ under some conditions on $Y$ and ${\rm deg} \, f$. |
| title | Morphisms from a very general hypersurface |
| topic | Algebraic Geometry 14E05, 14D05, 14J45, 14J70, 14M22 |
| url | https://arxiv.org/abs/1908.06894 |