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arXiv · 2604.02258

Pl\"ucker degrees of Quot schemes

Samuel Stark
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Abstract

We study the Pl\"{u}cker 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 Pl\"{u}cker degree. We also obtain a higher-dimensional analogue of a classical result of Schubert.

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Samuel Stark. 2026-04-02. Pl\"ucker degrees of Quot schemes. https://arxiv.org/abs/2604.02258

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