Generic curves and non-coprime Catalans
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909227292819456 |
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| author | Gorsky, Eugene Mazin, Mikhail Oblomkov, Alexei |
| author_facet | Gorsky, Eugene Mazin, Mikhail Oblomkov, Alexei |
| contents | We compute the Poincaré polynomials of the compactified Jacobians for plane curve singularities with Puiseaux exponents $(nd,md,md+1)$, and relate them to the combinatorics of $q,t$-Catalan numbers in the non-coprime case. We also confirm a conjecture of Cherednik and Danilenko for such curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_12569 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generic curves and non-coprime Catalans Gorsky, Eugene Mazin, Mikhail Oblomkov, Alexei Algebraic Geometry Combinatorics We compute the Poincaré polynomials of the compactified Jacobians for plane curve singularities with Puiseaux exponents $(nd,md,md+1)$, and relate them to the combinatorics of $q,t$-Catalan numbers in the non-coprime case. We also confirm a conjecture of Cherednik and Danilenko for such curves. |
| title | Generic curves and non-coprime Catalans |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2210.12569 |