Discriminants and motivic integration
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913775946301440 |
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| author | Kivinen, Oscar Oblomkov, Alexei Wyss, Dimitri |
| author_facet | Kivinen, Oscar Oblomkov, Alexei Wyss, Dimitri |
| contents | We study invariants of a plane cuve singularity $(f,0)$ coming from motivic integration on symmetric powers of a formal deformation of $f$. We show that a natural discriminant integral recovers the motivic classes of the principal Hilbert schemes of points on $f$, while the orbifold integral gives the plethystic exponential of the motivic Igusa zeta function of $f$. The latter result also holds in higher dimemsions.
Combined with results of Gorsky and Némethi we obtain an interpretation of the discriminant integrals in terms of knot Floer homology, which is reminiscent of the relation between the cohomology of contact loci and fixed point Floer homology proven by de la Bodega and Poza. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18449 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discriminants and motivic integration Kivinen, Oscar Oblomkov, Alexei Wyss, Dimitri Algebraic Geometry We study invariants of a plane cuve singularity $(f,0)$ coming from motivic integration on symmetric powers of a formal deformation of $f$. We show that a natural discriminant integral recovers the motivic classes of the principal Hilbert schemes of points on $f$, while the orbifold integral gives the plethystic exponential of the motivic Igusa zeta function of $f$. The latter result also holds in higher dimemsions. Combined with results of Gorsky and Némethi we obtain an interpretation of the discriminant integrals in terms of knot Floer homology, which is reminiscent of the relation between the cohomology of contact loci and fixed point Floer homology proven by de la Bodega and Poza. |
| title | Discriminants and motivic integration |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2503.18449 |