Asymptotic base loci on hyper-Kähler manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911932755214336 |
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| author | Denisi, Francesco Antonio Ortiz, Ángel David Ríos |
| author_facet | Denisi, Francesco Antonio Ortiz, Ángel David Ríos |
| contents | Given a projective hyper-Kähler manifold $X$, we study the asymptotic base loci of big divisors on $X$. We provide a numerical characterization of these loci and study how they vary while moving a big divisor class in the big cone, using the divisorial Zariski decomposition, and the Beauville-Bogomolov-Fujiki form. We determine the dual of the cones of $k$-ample divisors $\mathrm{Amp}_k(X)$, for any $1\leq k \leq \mathrm{dim}(X)$, answering affirmatively (in the case of projective hyper-Kähler manifolds) a question asked by Sam Payne. We provide a decomposition for the effective cone $\mathrm{Eff}(X)$ into chambers of Mori-type, analogous to that for Mori dream spaces into Mori chambers. To conclude, we illustrate our results with several examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01773 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic base loci on hyper-Kähler manifolds Denisi, Francesco Antonio Ortiz, Ángel David Ríos Algebraic Geometry Given a projective hyper-Kähler manifold $X$, we study the asymptotic base loci of big divisors on $X$. We provide a numerical characterization of these loci and study how they vary while moving a big divisor class in the big cone, using the divisorial Zariski decomposition, and the Beauville-Bogomolov-Fujiki form. We determine the dual of the cones of $k$-ample divisors $\mathrm{Amp}_k(X)$, for any $1\leq k \leq \mathrm{dim}(X)$, answering affirmatively (in the case of projective hyper-Kähler manifolds) a question asked by Sam Payne. We provide a decomposition for the effective cone $\mathrm{Eff}(X)$ into chambers of Mori-type, analogous to that for Mori dream spaces into Mori chambers. To conclude, we illustrate our results with several examples. |
| title | Asymptotic base loci on hyper-Kähler manifolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2304.01773 |