The number of smooth varieties in an MMP on a 3-fold of Fano type
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911737078349824 |
|---|---|
| author | Kim, Donghyeon |
| author_facet | Kim, Donghyeon |
| contents | In this paper, we prove that for a threefold of Fano type $X$ and a movable $\mathbb{Q}$-Cartier Weil divisor $D$ on $X$, the number of smooth varieties that arise during the running of a $D$-MMP is bounded by $1 + h^1(X, 2D)$. Additionally, we prove a partial converse to the Kodaira vanishing theorem for a movable divisor on a threefold of Fano type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The number of smooth varieties in an MMP on a 3-fold of Fano type Kim, Donghyeon Algebraic Geometry 14E30, 14F17 In this paper, we prove that for a threefold of Fano type $X$ and a movable $\mathbb{Q}$-Cartier Weil divisor $D$ on $X$, the number of smooth varieties that arise during the running of a $D$-MMP is bounded by $1 + h^1(X, 2D)$. Additionally, we prove a partial converse to the Kodaira vanishing theorem for a movable divisor on a threefold of Fano type. |
| title | The number of smooth varieties in an MMP on a 3-fold of Fano type |
| topic | Algebraic Geometry 14E30, 14F17 |
| url | https://arxiv.org/abs/2502.01370 |