Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.16632 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918208473137152 |
|---|---|
| author | Jiang, Chen Liu, Haidong Liu, Jie |
| author_facet | Jiang, Chen Liu, Haidong Liu, Jie |
| contents | We show that for a $\mathbb Q$-factorial canonical Fano $3$-fold $X$ of Picard number $1$, $(-K_X)^3\leq 72$. The main tool is a Kawamata--Miyaoka type inequality which relates $(-K_X)^3$ with $\hat{c}_2(X)\cdot c_1(X)$, where $\hat{c}_2(X)$ is the generalized second Chern class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal upper bound for degrees of canonical Fano threefolds of Picard number one Jiang, Chen Liu, Haidong Liu, Jie Algebraic Geometry We show that for a $\mathbb Q$-factorial canonical Fano $3$-fold $X$ of Picard number $1$, $(-K_X)^3\leq 72$. The main tool is a Kawamata--Miyaoka type inequality which relates $(-K_X)^3$ with $\hat{c}_2(X)\cdot c_1(X)$, where $\hat{c}_2(X)$ is the generalized second Chern class. |
| title | Optimal upper bound for degrees of canonical Fano threefolds of Picard number one |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2501.16632 |