Singularities of diagonals of Laurent series for rational functions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911586733522944 |
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| author | Pochekutov, Dmitriy |
| author_facet | Pochekutov, Dmitriy |
| contents | We study the complete diagonal of the Laurent series expansion of a rational function in $n$-complex variables. For a denominator that is nondegenerate for its Newton polyhedron, we prove that the complete diagonal, initially defined in a logarithmically convex domain, can be analytically continued along any path in the $r$-dimensional complex torus that avoids an explicitly defined complex analytic set $L$ called the Landau variety. This variety is constructed as the union of discriminants associated with specific truncations of the denominator to the faces of its Newton polyhedron. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10605 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Singularities of diagonals of Laurent series for rational functions Pochekutov, Dmitriy Complex Variables Algebraic Geometry 32D15 (Primary) 32A05, 32A27 (Secondary) We study the complete diagonal of the Laurent series expansion of a rational function in $n$-complex variables. For a denominator that is nondegenerate for its Newton polyhedron, we prove that the complete diagonal, initially defined in a logarithmically convex domain, can be analytically continued along any path in the $r$-dimensional complex torus that avoids an explicitly defined complex analytic set $L$ called the Landau variety. This variety is constructed as the union of discriminants associated with specific truncations of the denominator to the faces of its Newton polyhedron. |
| title | Singularities of diagonals of Laurent series for rational functions |
| topic | Complex Variables Algebraic Geometry 32D15 (Primary) 32A05, 32A27 (Secondary) |
| url | https://arxiv.org/abs/2604.10605 |