Extremal Contraction of Projective Bundles
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914943496880128 |
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| author | Bansal, Ashima Sarkar, Supravat Vats, Shivam |
| author_facet | Bansal, Ashima Sarkar, Supravat Vats, Shivam |
| contents | In this article, we explore the extremal contractions of several projective bundles over smooth Fano varieties of Picard rank $1$. We provide a whole class of examples of projective bundles with smooth blow-up structures, derived from the notion of drums which was introduced by Occhetta-Romano-Conde-Wiśniewski to study interaction with $\mathbb{C}^*$-actions and birational geometry. By manipulating projective bundles, we give a simple geometric construction of the rooftop flip, which was introduced recently by Barban-Franceschini. Additionally, we obtain analogues of some recent results of Vats in higher dimensions. The list of projective bundles we consider includes all globally generated bundles over projective space with first Chern class $2$. For each of them, we compute the nef and pseudoeffective cones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05091 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extremal Contraction of Projective Bundles Bansal, Ashima Sarkar, Supravat Vats, Shivam Algebraic Geometry 14E30, 14E05 In this article, we explore the extremal contractions of several projective bundles over smooth Fano varieties of Picard rank $1$. We provide a whole class of examples of projective bundles with smooth blow-up structures, derived from the notion of drums which was introduced by Occhetta-Romano-Conde-Wiśniewski to study interaction with $\mathbb{C}^*$-actions and birational geometry. By manipulating projective bundles, we give a simple geometric construction of the rooftop flip, which was introduced recently by Barban-Franceschini. Additionally, we obtain analogues of some recent results of Vats in higher dimensions. The list of projective bundles we consider includes all globally generated bundles over projective space with first Chern class $2$. For each of them, we compute the nef and pseudoeffective cones. |
| title | Extremal Contraction of Projective Bundles |
| topic | Algebraic Geometry 14E30, 14E05 |
| url | https://arxiv.org/abs/2409.05091 |