A Kawamata--Miyaoka type inequality for Fano varieties of arbitrary Picard number
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912715134468096 |
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| author | Liu, Haidong |
| author_facet | Liu, Haidong |
| contents | Let $X$ be a $\mathbb Q$-factorial canonical weak Fano variety of dimension $n\geq 2$. We show that if the $\mathbb Q$-Fano index $q_{\mathbb Q}(X)\geq 3$, then $X$ satisfies a Kawamata--Miyaoka type inequality: \[c_1(X)^n\leq 4\,\hat c_2(X)\cdot c_1(X)^{n-2}.\] As an application, we show that the $\mathbb Q$-Fano index of a Gorenstein canonical Fano $3$-fold lies in the set $\{m\in\mathbb Z_{>0}\mid m\leq 22\} \cup\{24,30,42\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Kawamata--Miyaoka type inequality for Fano varieties of arbitrary Picard number Liu, Haidong Algebraic Geometry Let $X$ be a $\mathbb Q$-factorial canonical weak Fano variety of dimension $n\geq 2$. We show that if the $\mathbb Q$-Fano index $q_{\mathbb Q}(X)\geq 3$, then $X$ satisfies a Kawamata--Miyaoka type inequality: \[c_1(X)^n\leq 4\,\hat c_2(X)\cdot c_1(X)^{n-2}.\] As an application, we show that the $\mathbb Q$-Fano index of a Gorenstein canonical Fano $3$-fold lies in the set $\{m\in\mathbb Z_{>0}\mid m\leq 22\} \cup\{24,30,42\}$. |
| title | A Kawamata--Miyaoka type inequality for Fano varieties of arbitrary Picard number |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2511.13425 |