On quadratic persistence and Pythagoras numbers of totally real projective varieties
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918060126896128 |
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| author | Han, Jong In Jung, Jaewoo Park, Euisung |
| author_facet | Han, Jong In Jung, Jaewoo Park, Euisung |
| contents | In this paper, we study the relationship between quadratic persistence and the Pythagoras number of totally real projective varieties. Building upon the foundational work of Blekherman et al. in arXiv:1902.02754, we extend their characterizations of arithmetically Cohen-Macaulay varieties with next-to-maximal quadratic persistence to arbitrary case. Our main result classifies totally real non-aCM varieties of codimension $c$ and degree $d$ that exhibit next-to-maximal quadratic persistence in the cases where $c=3$ and $d \geq 6$ or $c \geq 4$ and $d \geq 2c+3$. We further investigate the quadratic persistence and Pythagoras number in the context of curves of maximal regularity and linearly normal smooth curves of genus 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On quadratic persistence and Pythagoras numbers of totally real projective varieties Han, Jong In Jung, Jaewoo Park, Euisung Algebraic Geometry Commutative Algebra 14P05, 14N05, 14Q30, 13D02 In this paper, we study the relationship between quadratic persistence and the Pythagoras number of totally real projective varieties. Building upon the foundational work of Blekherman et al. in arXiv:1902.02754, we extend their characterizations of arithmetically Cohen-Macaulay varieties with next-to-maximal quadratic persistence to arbitrary case. Our main result classifies totally real non-aCM varieties of codimension $c$ and degree $d$ that exhibit next-to-maximal quadratic persistence in the cases where $c=3$ and $d \geq 6$ or $c \geq 4$ and $d \geq 2c+3$. We further investigate the quadratic persistence and Pythagoras number in the context of curves of maximal regularity and linearly normal smooth curves of genus 3. |
| title | On quadratic persistence and Pythagoras numbers of totally real projective varieties |
| topic | Algebraic Geometry Commutative Algebra 14P05, 14N05, 14Q30, 13D02 |
| url | https://arxiv.org/abs/2506.13247 |