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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2405.14553 |
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| _version_ | 1866910457843941376 |
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| author | Bini, Gilberto Brambilla, Maria Chiara Fontanari, Claudio Postinghel, Elisa |
| author_facet | Bini, Gilberto Brambilla, Maria Chiara Fontanari, Claudio Postinghel, Elisa |
| contents | Let $\overline{\mathrm{Mov}}^k(X)$ be the closure of the cone $\mathrm{Mov}^k(X)$ generated by classes of effective divisors on a projective variety $X$ with stable base locus of codimension at least $k+1$. We propose a generalized version of the Log Nonvanishing Conjecture and of the Log Abundance Conjecture for a klt pair $(X,Δ)$, that is: if $K_X+Δ\in \overline{\mathrm{Mov}}^{k}(X)$, then $K_X+Δ\in \mathrm{Mov}^{k}(X)$. Moreover, we prove that if the Log Minimal Model Program, the Log Nonvanishing, and the Log Abundance hold, then so does our conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14553 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonvanishing and Abundance for cones of movable divisors Bini, Gilberto Brambilla, Maria Chiara Fontanari, Claudio Postinghel, Elisa Algebraic Geometry Let $\overline{\mathrm{Mov}}^k(X)$ be the closure of the cone $\mathrm{Mov}^k(X)$ generated by classes of effective divisors on a projective variety $X$ with stable base locus of codimension at least $k+1$. We propose a generalized version of the Log Nonvanishing Conjecture and of the Log Abundance Conjecture for a klt pair $(X,Δ)$, that is: if $K_X+Δ\in \overline{\mathrm{Mov}}^{k}(X)$, then $K_X+Δ\in \mathrm{Mov}^{k}(X)$. Moreover, we prove that if the Log Minimal Model Program, the Log Nonvanishing, and the Log Abundance hold, then so does our conjecture. |
| title | Nonvanishing and Abundance for cones of movable divisors |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2405.14553 |