Log-concavity from enumerative geometry of planar curve singularities
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918476165152768 |
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| author | Su, Tao Xie, Baiting Yu, Chenglong |
| author_facet | Su, Tao Xie, Baiting Yu, Chenglong |
| contents | We propose a log-concavity conjecture for BPS invariants arising in the enumerative geometry of planar curve singularities, identified with the local Euler obstructions of Severi strata in their versal deformations. We further extend this conjecture to ruling polynomials of Legendrian links and to E-polynomials of character varieties. We establish these conjectures for irreducible weighted-homogeneous singularities (torus knots) and for ADE singularities, and prove a multiplicative property for ruling polynomials compatible with log-concavity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_27888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Log-concavity from enumerative geometry of planar curve singularities Su, Tao Xie, Baiting Yu, Chenglong Algebraic Geometry Combinatorics Symplectic Geometry 14N10, 14H20 (Primary) 57K10, 14F43, 14D15 (Secondary) We propose a log-concavity conjecture for BPS invariants arising in the enumerative geometry of planar curve singularities, identified with the local Euler obstructions of Severi strata in their versal deformations. We further extend this conjecture to ruling polynomials of Legendrian links and to E-polynomials of character varieties. We establish these conjectures for irreducible weighted-homogeneous singularities (torus knots) and for ADE singularities, and prove a multiplicative property for ruling polynomials compatible with log-concavity. |
| title | Log-concavity from enumerative geometry of planar curve singularities |
| topic | Algebraic Geometry Combinatorics Symplectic Geometry 14N10, 14H20 (Primary) 57K10, 14F43, 14D15 (Secondary) |
| url | https://arxiv.org/abs/2603.27888 |