Characterization of products of projective spaces via nef complexity
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917147687518208 |
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| author | Enwright, Joshua Filipazzi, Stefano Gongyo, Yoshinori Moraga, Joaquín Svaldi, Roberto Wang, Chengxi Watanabe, Kiwamu |
| author_facet | Enwright, Joshua Filipazzi, Stefano Gongyo, Yoshinori Moraga, Joaquín Svaldi, Roberto Wang, Chengxi Watanabe, Kiwamu |
| contents | We define the nef complexity of a projective variety $X$. This invariant compares $\dim X+ρ(X)$ with the sum of the coefficients of nef partitions of $-K_X$. We prove that the nef complexity is non-negative and it is zero precisely for products of projective spaces. We classify smooth Fano threefolds with nef complexity at most one. In a similar vein, we prove Mukai's conjecture for smooth Fano varieties for which every extremal contraction is of fiber type and study smooth images of products of projective spaces. Along the way, we answer positively a question of J. Starr regarding the nef cone of smooth Fano varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of products of projective spaces via nef complexity Enwright, Joshua Filipazzi, Stefano Gongyo, Yoshinori Moraga, Joaquín Svaldi, Roberto Wang, Chengxi Watanabe, Kiwamu Algebraic Geometry Primary 14J45, Secondary 14E30 We define the nef complexity of a projective variety $X$. This invariant compares $\dim X+ρ(X)$ with the sum of the coefficients of nef partitions of $-K_X$. We prove that the nef complexity is non-negative and it is zero precisely for products of projective spaces. We classify smooth Fano threefolds with nef complexity at most one. In a similar vein, we prove Mukai's conjecture for smooth Fano varieties for which every extremal contraction is of fiber type and study smooth images of products of projective spaces. Along the way, we answer positively a question of J. Starr regarding the nef cone of smooth Fano varieties. |
| title | Characterization of products of projective spaces via nef complexity |
| topic | Algebraic Geometry Primary 14J45, Secondary 14E30 |
| url | https://arxiv.org/abs/2512.13637 |