Real regulator maps with finite 0-locus
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914426086490112 |
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| author | Acuna, RJ Akman, Devin Kerr, Matt |
| author_facet | Acuna, RJ Akman, Devin Kerr, Matt |
| contents | A Laurent polynomial in two variables is tempered if its edge polynomials are cyclotomic. Variation of coefficients leads to a family of smooth complete genus $g$ curves carrying a canonical algebraic $K_2$-class over a $g$-dimensional base $S$, hence to an extension of admissible variations of MHS (or normal function) on $S$. We prove that the $\mathbb{R}$-split locus of this extension is finite. Consequently, the torsion locus of the normal function and the $A$-polynomial locus for the family of curves are also finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10392 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real regulator maps with finite 0-locus Acuna, RJ Akman, Devin Kerr, Matt Algebraic Geometry 14C30, 14D07, 32G20 A Laurent polynomial in two variables is tempered if its edge polynomials are cyclotomic. Variation of coefficients leads to a family of smooth complete genus $g$ curves carrying a canonical algebraic $K_2$-class over a $g$-dimensional base $S$, hence to an extension of admissible variations of MHS (or normal function) on $S$. We prove that the $\mathbb{R}$-split locus of this extension is finite. Consequently, the torsion locus of the normal function and the $A$-polynomial locus for the family of curves are also finite. |
| title | Real regulator maps with finite 0-locus |
| topic | Algebraic Geometry 14C30, 14D07, 32G20 |
| url | https://arxiv.org/abs/2407.10392 |