Plücker degrees of Quot schemes
We study the degree of the Plücker embedding $\varpi$ 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 $\mathrm{deg} \ \varpi$. We also obtain a higher-dimensional analogue of a classical result of Schubert.
Authors: Samuel Stark
Citations: N/A
Published: 2026-04-02T16:52:45Z
Abstract
We study the degree of the Plücker embedding $\varpi$ 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 $\mathrm{deg} \ \varpi$. We also obtain a higher-dimensional analogue of a classical result of Schubert.
Paper → Strategy Transfer
Convert this paper from passive reading into a mechanism, signal idea, failure mode, and strategy object candidate.
Ask RAG about this object
Pull basis, related strategy objects, and route targets from the shared Ztrader memory layer.