Curves on complete intersections and measures of irrationality
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929388853919744 |
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| author | Chen, Nathan Church, Benjamin Zhao, Junyan |
| author_facet | Chen, Nathan Church, Benjamin Zhao, Junyan |
| contents | We study the minimal degrees and gonalities of curves on complete intersections. We prove a classical conjecture which asserts that the degree of any curve on a general complete intersection $X \subseteq \mathbb{P}^N$ cut out by polynomials of large degrees is bounded from below by the degree of $X$. As an application, we verify a conjecture of Bastianelli--De Poi--Ein--Lazarsfeld--Ullery on measures of irrationality for complete intersections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12101 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curves on complete intersections and measures of irrationality Chen, Nathan Church, Benjamin Zhao, Junyan Algebraic Geometry 14D06, 14J70 We study the minimal degrees and gonalities of curves on complete intersections. We prove a classical conjecture which asserts that the degree of any curve on a general complete intersection $X \subseteq \mathbb{P}^N$ cut out by polynomials of large degrees is bounded from below by the degree of $X$. As an application, we verify a conjecture of Bastianelli--De Poi--Ein--Lazarsfeld--Ullery on measures of irrationality for complete intersections. |
| title | Curves on complete intersections and measures of irrationality |
| topic | Algebraic Geometry 14D06, 14J70 |
| url | https://arxiv.org/abs/2406.12101 |