Free curves and fundamental groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866915716300537856 |
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| author | Jovinelly, Eric Lehmann, Brian Riedl, Eric |
| author_facet | Jovinelly, Eric Lehmann, Brian Riedl, Eric |
| contents | We show that klt Fano varieties and certain lc Fano varieties contain free higher-genus curves in their smooth loci. Our methods also allow us to find free curves on varieties in positive characteristic and on quasiprojective varieties, under a natural positivity condition on the tangent bundle. We then use the existence of free curves to deduce finiteness of the fundamental group of the smooth locus in these settings.
The paper includes an appendix by de Jong that establishes the Künneth formula for tame étale fundamental groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27031 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free curves and fundamental groups Jovinelly, Eric Lehmann, Brian Riedl, Eric Algebraic Geometry We show that klt Fano varieties and certain lc Fano varieties contain free higher-genus curves in their smooth loci. Our methods also allow us to find free curves on varieties in positive characteristic and on quasiprojective varieties, under a natural positivity condition on the tangent bundle. We then use the existence of free curves to deduce finiteness of the fundamental group of the smooth locus in these settings. The paper includes an appendix by de Jong that establishes the Künneth formula for tame étale fundamental groups. |
| title | Free curves and fundamental groups |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2510.27031 |