Plücker degrees of Quot schemes
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910152029896704 |
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| author | Stark, Samuel |
| author_facet | Stark, Samuel |
| contents | We study the Plücker degree of the main component of the Quot scheme of length $l$ quotients of a locally free sheaf on a smooth projective scheme $\mathrm{S}$ of dimension $d\geqslant 1$. This degree is determined by classes in the Chow ring of the symmetric product $\mathrm{S}^{(l)}$, which are given by the pushforward of the powers of $c_{1}(\mathcal{O}^{[l]})$ with respect to the canonical morphism from the Quot scheme to $\mathrm{S}^{(l)}$. We describe a decomposition of these classes, allowing us to compute the (in a certain sense) leading term of the Plücker degree. We also obtain a higher-dimensional analogue of a classical result of Schubert. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02258 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Plücker degrees of Quot schemes Stark, Samuel Algebraic Geometry We study the Plücker degree of the main component of the Quot scheme of length $l$ quotients of a locally free sheaf on a smooth projective scheme $\mathrm{S}$ of dimension $d\geqslant 1$. This degree is determined by classes in the Chow ring of the symmetric product $\mathrm{S}^{(l)}$, which are given by the pushforward of the powers of $c_{1}(\mathcal{O}^{[l]})$ with respect to the canonical morphism from the Quot scheme to $\mathrm{S}^{(l)}$. We describe a decomposition of these classes, allowing us to compute the (in a certain sense) leading term of the Plücker degree. We also obtain a higher-dimensional analogue of a classical result of Schubert. |
| title | Plücker degrees of Quot schemes |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.02258 |