Abundance for varieties with many differential forms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866918127985491968 |
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| author | Lazić, Vladimir Peternell, Thomas |
| author_facet | Lazić, Vladimir Peternell, Thomas |
| contents | We prove that the abundance conjecture holds on a variety $X$ with mild singularities if $X$ has many reflexive differential forms with coefficients in pluricanonical bundles, assuming the Minimal Model Program in lower dimensions. This implies, for instance, that under this condition, hermitian semipositive canonical divisors are almost always semiample, and that klt pairs whose underlying variety is uniruled have good models in many circumstances. When the numerical dimension of $K_X$ is $1$, our results hold unconditionally in every dimension. We also treat a related problem on the semiampleness of nef line bundles on Calabi-Yau varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1601_01602 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Abundance for varieties with many differential forms Lazić, Vladimir Peternell, Thomas Algebraic Geometry 14E30, 14F10 We prove that the abundance conjecture holds on a variety $X$ with mild singularities if $X$ has many reflexive differential forms with coefficients in pluricanonical bundles, assuming the Minimal Model Program in lower dimensions. This implies, for instance, that under this condition, hermitian semipositive canonical divisors are almost always semiample, and that klt pairs whose underlying variety is uniruled have good models in many circumstances. When the numerical dimension of $K_X$ is $1$, our results hold unconditionally in every dimension. We also treat a related problem on the semiampleness of nef line bundles on Calabi-Yau varieties. |
| title | Abundance for varieties with many differential forms |
| topic | Algebraic Geometry 14E30, 14F10 |
| url | https://arxiv.org/abs/1601.01602 |