On the embedded Nash problem
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866909395028279296 |
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| author | Budur, Nero de la Bodega, Javier Poza, Eduardo de Lorenzo de Bobadilla, Javier Fernández Pełka, Tomasz |
| author_facet | Budur, Nero de la Bodega, Javier Poza, Eduardo de Lorenzo de Bobadilla, Javier Fernández Pełka, Tomasz |
| contents | The embedded Nash problem for a hypersurface in a smooth algebraic variety, is to characterize geometrically the maximal irreducible families of arcs with fixed order of contact along the hypersurface. We show that divisors on minimal models of the pair contribute with such families. We solve the problem for unibranch plane curve germs, in terms of the resolution graph. These are embedded analogs of known results for the classical Nash problem on singular varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_08546 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the embedded Nash problem Budur, Nero de la Bodega, Javier Poza, Eduardo de Lorenzo de Bobadilla, Javier Fernández Pełka, Tomasz Algebraic Geometry The embedded Nash problem for a hypersurface in a smooth algebraic variety, is to characterize geometrically the maximal irreducible families of arcs with fixed order of contact along the hypersurface. We show that divisors on minimal models of the pair contribute with such families. We solve the problem for unibranch plane curve germs, in terms of the resolution graph. These are embedded analogs of known results for the classical Nash problem on singular varieties. |
| title | On the embedded Nash problem |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2208.08546 |